diff --git a/README-remember.md b/README-remember.md deleted file mode 100644 index 8ad5381..0000000 --- a/README-remember.md +++ /dev/null @@ -1,108 +0,0 @@ - - -Here's how you subclass. - - -```python -class sGT(GT): - """ - Example standard GT with Steve House-Style defaults. - - Each application can create its own defaults by subclassing GT - in this way. - """ - - def __init__(self, df, caption="", guess_years=True, ratio_regex='lr|roe|coc', **kwargs): - """Create Steve House-Style Formatter. Does not handle list of lists input.""" - if isinstance(df, str): - df, aligners_ = GT.md_to_df(df) - if 'aligners' not in kwargs: - kwargs['aligners'] = aligners_ - kwargs['show_index'] = False - - nindex = df.index.nlevels - ncolumns = df.columns.nlevels - if 'ratio_cols' in kwargs: - ratio_cols = kwargs['ratio_cols'] - else: - if ratio_regex != '' and ncolumns == 1: - ratio_cols = df.filter(regex=ratio_regex).columns.to_list() - else: - ratio_cols = None - - if guess_years: - year_cols = sGT.guess_years(df) - else: - year_cols = kwargs.get('year_cols', None) - - # rule sizes - hrule_widths = (1.5, 1, 0) if nindex > 1 else None - vrule_widths = (1.5, 1, 0.5) if ncolumns > 1 else None - - table_hrule_width = 1 if nindex == 1 else 2 - table_vrule_width = 1 if ncolumns == 1 else ( - 1.5 if ncolumns == 2 else 2) - - # padding - nr, nc = df.shape - if 'padding_trbl' in kwargs: - padding_trbl = kwargs['padding_trbl'] - else: - pad_tb = 4 if nr < 16 else (2 if nr < 25 else 1) - pad_lr = 10 if nc < 9 else (5 if nc < 13 else 2) - padding_trbl = (pad_tb, pad_lr, pad_tb, pad_lr) - - font_body = 0.9 if nr < 25 else (0.8 if nr < 41 else 0.7) - font_caption = np.round(1.1 * font_body, 2) - font_head = np.round(1.1 * font_body, 2) - - pef_lower = -3 - pef_upper = 6 - pef_precision = 3 - - defaults = { - 'ratio_cols': ratio_cols, - 'year_cols': year_cols, - 'default_integer_str': '{x:,.0f}', - 'default_float_str': '{x:,.3f}', - 'default_date_str': '%Y-%m-%d', - 'default_ratio_str': '{x:.1%}', - 'cast_to_floats': True, - 'table_hrule_width': table_hrule_width, - 'table_vrule_width': table_vrule_width, - 'hrule_widths': hrule_widths, - 'vrule_widths': vrule_widths, - 'sparsify': True, - 'sparsify_columns': True, - 'padding_trbl': padding_trbl, - 'font_body': font_body, - 'font_head': font_head, - 'font_caption': font_caption, - 'pef_precision': pef_precision, - 'pef_lower': pef_lower, - 'pef_upper': pef_upper, - 'debug': False - } - defaults.update(kwargs) - super().__init__(df, caption=caption, **defaults) - - @staticmethod - def guess_years(df): - """Try to guess which columns (body or index) are years. - - A column is considered a year if: - - It is numeric (integer or convertible to integer) - - All values are within a reasonable range (e.g., 1800–2100) - """ - year_columns = [] - df = df.reset_index(drop=False, col_level=df.columns.nlevels - 1) - for i, col in enumerate(df.columns): - try: - series = pd.to_numeric(df[col], errors='coerce').dropna() - if series.dtype.kind in 'iu' and series.between(1800, 2100).all(): - year_columns.append(col) - except Exception: - continue - return year_columns - -``` diff --git a/README.md b/README.md index 8839198..465bd80 100644 --- a/README.md +++ b/README.md @@ -1,5 +1,8 @@ sort out the variety of readmes... this is the main one +https://shields.io/badges/read-the-docs + + # v 3.0 update * config files @@ -195,12 +198,56 @@ More coming soon. ## Documentation +![](https://img.shields.io/readthedocs/greater_tables_project) + Available on [readthedocs](https://greater-tables-project.readthedocs.io/en/latest). ## Versions -### 1.1.1 +3.0.0 +------- + +2.0.0 +------ + +1.1.1 +------- * Added logo, updated docs. -### 1.1.0 +1.1.0 +------ + +* added ``formatters`` argument to pass in column specific formatters by name as a number (``n`` converts to ``{x:.nf}``, format string, or function +* Added ```tabs`` argument to provide column widths +* Added ``equal`` argument to provide hint that column widths should all be equal +* Added ``caption_align='center'`` argument to set the caption alignment +* Added ``large_ok=False`` argument, if ``False`` providing a dataframe with more than 100 rows throws an error. This function is expensive and is designed for small frames. + + +1.0.0 +------ + +* Allow input via list of lists, or markdown table +* Specify overall float format for whole table +* Specify column alingment with 'llrc' style string +* ``show_index`` option +* Added more tests +* Docs updated +* Set tabs for width; use of width in HTML format. + + +0.6.0 +------ + +* Initial release + +Early development +------------------- + +* 0.1.0 - 0.5.0: Early development +* tikz code from great.pres_manager + + + + diff --git a/README.qmd b/README.qmd deleted file mode 100644 index 284763c..0000000 --- a/README.qmd +++ /dev/null @@ -1,99 +0,0 @@ ---- -format: - pdf: - include-in-header: prefobnicate.tex - html: - table-processing: false -jupyter: - keep-ipynb: true - jupytext: - formats: ipynb,qmd - text_representation: - extension: .qmd - format_name: quarto - format_version: '1.0' - jupytext_version: 1.16.4 - kernelspec: - display_name: Python 3 (ipykernel) - language: python - name: python3 ---- - -# Greater Tables - -Creating presentation quality tables from pandas dataframes is frustrating. It is hard to left-align text and right-align numbers using pandas `display` or `df.to_html`. The `great_tables` package does a really nice job with pandas and polars dataframes but does not support indexes or TeX output. - -This package provides consistent HTML and TeX table output with flexible type-based formatting, and table rules. Neither output relies on the pandas `to_html` or `to_latex` functions. TeX output uses Tikz tables for very tight control over layout and grid lines. The package is designed for use in Jupyter Lab notebooks Quarto documents. - -Usage: the main class `GT` should be subclassed to set appropriate defaults for your project. `sGT` provides an example. - -The project is currently in **beta** status. HTML output is better developed than TeX. - -## The Name - -Obviously, the name is a play on the `great_tables` package. But, I have been maintaining a set of macros called [GREATools](https://www.mynl.com/old/GREAT/home.html) (generalized, reusable, extensible actuarial tools) in VBA and Python since the late 1990s, and call all my macro packages "GREAT". - -## Installation - -```python -pip install greater-tables -``` - -## Examples - -The following example shows quite a hard table. It is formatted using the `sGT` class, which is a subclass of `GT` with a few defaults set. - -```{python} -#| echo: true -#| output: asis -import pandas as pd -import numpy as np -from greater_tables import sGT -level_1 = ["Group A", "Group A", "Group B", "Group B", 'Group C'] -level_2 = ['Sub 1', 'Sub 2', 'Sub 2', 'Sub 3', 'Sub 3'] - -multi_index = pd.MultiIndex.from_arrays([level_1, level_2]) - -start = pd.Timestamp.today().normalize() # Today's date, normalized to midnight -end = pd.Timestamp(f"{start.year}-12-31") # End of the year - -hard = pd.DataFrame( -{'x': np.arange(2020, 2025, dtype=int), -'a': np.array((100, 105, 2000, 2025, 100000), dtype=int), -'b': 10. ** np.linspace(-9, 9, 5), -'c': np.linspace(601, 4000, 5), -'d': pd.date_range(start=start, end=end, periods=5), -'e': 'once upon a time, risk is hard to define, not in Kansas anymore, neutrinos are hard to detect, $\\int_\\infty^\\infty e^{-x^2/2}dx$ is a hard integral'.split(',') -}).set_index('x') -hard.columns = multi_index -sGT(hard, 'A hard table.') -``` - -![HTML output](hard_table_html.png) - -![TeX output](hard_table_tex.png) - -The output illustrates: - -* Quarto or Jupyter automatically the class's `_repr_html_` method (or `_repr_latex_` for pdf/TeX/Beamer output), providing seamless integration across different output formats. -* Text is left-aligned, numbers are right-aligned. -* The index is displayed, was detected as likely years, and formatted without a comma separator. -* The first column of integers does have a comma thousands separator. -* The second column of floats spans several orders of magnitude and is formatted using Engineering format, n for nano through G for giga. -* The third column of floats is formatted with a comma separator and two decimals, based on the average absolute value. -* The fourth column of date times is formatted as ISO standard dates (not date times). -* The vertical lines separate the levels of the column multiindex. The subgroups are a little tricky. - -More coming soon. - - -## Documentation - -Available on [readthedocs](https://greater-tables-project.readthedocs.io/en/latest). - -## Versions - -### 1.1.1 -* Added logo, updated docs. - -### 1.1.0 diff --git a/README.rst b/README.rst deleted file mode 100644 index bc75fe1..0000000 --- a/README.rst +++ /dev/null @@ -1,46 +0,0 @@ -.. image:: https://img.shields.io/readthedocs/greater_tables_project - :alt: Read the Docs - -Release Notes -=============== - -1.1.0 ------- - -* added ``formatters`` argument to pass in column specific formatters by name as a number (``n`` converts to ``{x:.nf}``, format string, or function -* Added ```tabs`` argument to provide column widths -* Added ``equal`` argument to provide hint that column widths should all be equal -* Added ``caption_align='center'`` argument to set the caption alignment -* Added ``large_ok=False`` argument, if ``False`` providing a dataframe with more than 100 rows throws an error. This function is expensive and is designed for small frames. - - -1.0.0 ------- - -* Allow input via list of lists, or markdown table -* Specify overall float format for whole table -* Specify column alingment with 'llrc' style string -* ``show_index`` option -* Added more tests -* Docs updated -* Set tabs for width; use of width in HTML format. - - -0.6.0 ------- - -* Initial release - -Early development -------------------- - -* 0.1.0 - 0.5.0: Early development -* tikz code from great.pres_manager - -TODO -===== - -* Index aligners - - -https://shields.io/badges/read-the-docs \ No newline at end of file diff --git a/greater_tables/greater_tables.py b/greater_tables/greater_tables.py index 67dad1a..a921937 100644 --- a/greater_tables/greater_tables.py +++ b/greater_tables/greater_tables.py @@ -23,6 +23,7 @@ from rich import box from rich.table import Table from . hasher import df_short_hash +from . gtformats import GT_Format, TableFormat # turn this fuck-fest off pd.set_option('future.no_silent_downcasting', True) @@ -61,43 +62,6 @@ class Breakability(IntEnum): ACCEPTABLE = 10 -# specify text mode -Line = namedtuple('Line', ['begin', 'hline', 'sep', 'end', 'index_sep']) -DataRow = namedtuple('DataRow', ['begin', 'sep', 'end', 'index_sep']) -TableFormat = namedtuple('TableFormat', [ - 'lineabove', - 'linebelowheader', - 'linebetweenrows', - 'linebelow', - 'headerrow', - 'datarow', - 'padding', - 'with_header_hide' -]) - -# generic text format -GT_Format = TableFormat( - lineabove=Line('┍', '━', '┯', '┑', '┳'), - linebelowheader=Line('┝', '━', '┿', '┥', '╋'), - linebetweenrows=Line('├', '─', '┼', '┤', '╂'), - linebelow=Line('┕', '━', '┷', '┙', '┻'), - headerrow=DataRow('│', '│', '│', '┃'), - datarow=DataRow('│', '│', '│', '┃'), - padding=1, - with_header_hide=None -) - -# GT_Format = TableFormat( -# lineabove=Line('\u250d', '\u2501', '\u252f', '\u2511', '\u2533'), -# linebelowheader=Line('\u251d', '\u2501', '\u253f', '\u2525', '\u254b'), -# linebetweenrows=Line('\u251c', '\u2500', '\u253c', '\u2524', '\u2502'), -# linebelow=Line('\u2515', '\u2501', '\u2537', '\u2519', '\u253b'), -# headerrow=DataRow('\u2502', '\u2502', '\u2502', '\u2503'), -# datarow=DataRow('\u2502', '\u2502', '\u2502', '\u2503'), -# padding=1, -# with_header_hide=None -# ) - class GT(object): """ @@ -1716,7 +1680,10 @@ class GT(object): # dx = data in index # if this is the level that changes for this row # will use a top rule hence omit i = 0 which already has an hrule - if i > 0 and hrule == '' and j == index_change_level[i]: + # here have to be careful - if the index is not ! then not every row + # appears in the index change level. But if it DOES NOT appear then + # it isn't a change level so no rule required + if i > 0 and hrule == '' and i in index_change_level and j == index_change_level[i]: hrule = f'grt-hrule-{j}' # html.append(f'{c}') col_id = f'grt-c-{j}' diff --git a/greater_tables/gtcore2.py b/greater_tables/gtcore2.py index d9c108b..5c51ff7 100644 --- a/greater_tables/gtcore2.py +++ b/greater_tables/gtcore2.py @@ -18,18 +18,21 @@ import sys from textwrap import wrap from typing import Optional, Union, Literal import warnings +import yaml from bs4 import BeautifulSoup from cachetools import LRUCache import numpy as np import pandas as pd +from pandas.errors import IntCastingNaNError from pandas.api.types import is_datetime64_any_dtype, is_integer_dtype, \ is_float_dtype # , is_numeric_dtype +from pydantic import ValidationError from rich import box from rich.table import Table from . gtenums import Breakability, Alignment -from . gtformats import GT_Format, TableFormat +from . gtformats import GT_Format, TableFormat, Line, DataRow from . gtconfig import GTConfigModel from . hasher import df_short_hash @@ -242,7 +245,8 @@ class GT(object): **overrides, ): if config and config_path: - raise ValueError("Pass either 'config' or 'config_path', not both.") + raise ValueError( + "Pass either 'config' or 'config_path', not both.") if config: base_config = config @@ -251,7 +255,8 @@ class GT(object): raw = yaml.safe_load(config_path.read_text(encoding="utf-8")) base_config = GTConfigModel.model_validate(raw) except (ValidationError, OSError) as e: - raise ValueError(f"Failed to load config from {config_path}") from e + raise ValueError(f"Failed to load config from { + config_path}") from e else: base_config = GTConfigModel() @@ -402,7 +407,7 @@ class GT(object): self.raw_cols = raw_cols # figure the default formatter (used in conjunction with raw columns) - if config.default_formatter is None: + if self.config.default_formatter is None: self.default_formatter = self.default_formatter else: assert callable( @@ -413,13 +418,13 @@ class GT(object): return config.default_formatter(x) except ValueError: return str(x) - self.default_formatter = wrapped_config.default_formatter + self.default_formatter = wrapped_default_formatter # cast as much as possible to floats with warnings.catch_warnings(): warnings.simplefilter( "ignore", category=pd.errors.PerformanceWarning) - if config.cast_to_floats: + if self.config.cast_to_floats: for i, c in enumerate(self.df.columns): if c in self.raw_cols or c in self.date_cols: continue @@ -552,10 +557,10 @@ class GT(object): # self.default_float_formatter = None # self.hrule_widths = hrule_widths or (0, 0, 0) # if not isinstance(self.config.hrule_widths, (list, tuple)): - # self.config.hrule_widths = (self.config.hrule_widths,) + # self.config.hrule_widths = (self.config.hrule_widths,) # self.vrule_widths = vrule_widths or (0, 0, 0) # if not isinstance(self.config.hrule_widths, (list, tuple)): - # self.config.hrule_widths = (self.config.hrule_widths, ) + # self.config.hrule_widths = (self.config.hrule_widths, ) # self.table_hrule_width = table_hrule_width # self.table_vrule_width = table_vrule_width # self.font_body = font_body @@ -570,28 +575,25 @@ class GT(object): elif isinstance(tabs, (int, float)): self.tabs = (tabs,) elif isinstance(tabs, (np.ndarray, list, tuple)): - self.tabs = tabs # Already iterable, self.config.tabs = as is + self.tabs = tabs # Already iterable, self.tabs = as is else: self.tabs = [tabs] # Fallback for anything else # self.equal = equal - if config.padding_trbl is None: - if config.spacing == 'tight': - config.padding_trbl = (0, 5, 0, 5) - elif config.spacing == 'medium': - config.padding_trbl = (2, 10, 2, 10) - elif config.spacing == 'wide': - config.padding_trbl = (4, 15, 4, 15) + if self.config.padding_trbl is not None: + padding_trbl = self.config_padding_trbl + elif self.config.padding_trbl is None: + if self.config.spacing == 'tight': + padding_trbl = (0, 5, 0, 5) + elif self.config.spacing == 'medium': + padding_trbl = (2, 10, 2, 10) + elif self.config.spacing == 'wide': + padding_trbl = (4, 15, 4, 15) else: raise ValueError( 'config.spacing must be tight, medium, or wide or tuple of four ints.') - try: - self.padt, self.padr, self.padb, self.padl = config.padding_trbl - except ValueError: - # pydantics will see to this... - logger.error( - f'config.padding_trbl {config.padding_trbl=}, must be four ints, defaulting to medium padding') - self.padt, self.padr, self.padb, self.padl = 2, 10, 2, 10 + # pydantic will see to it this is OK + self.padt, self.padr, self.padb, self.padl = padding_trbl # because of the problem of non-unique indexes use a list and # not a dict to pass the formatters to to_html @@ -608,7 +610,7 @@ class GT(object): # cache for various things... self._cache = LRUCache(20) # config.sparsify - if config.sparsify and self.nindex > 1: + if self.config.sparsify and self.nindex > 1: self.df = GT.sparsify(self.df, self.df.columns[:self.nindex]) # for c in self.df.columns[:self.nindex]: # # config.sparsify returns some other stuff... @@ -857,7 +859,7 @@ class GT(object): self.default_float_formatter or self.make_float_formatter(self.df.iloc[:, i])) else: # print(f'{i} default') - self._df_formatters.append(self.config.default_formatter) + self._df_formatters.append(self.default_formatter) # self._df_formatters is now a list of length config.equal to cols in df if len(self._df_formatters) != self.df.shape[1]: raise ValueError( @@ -925,8 +927,10 @@ class GT(object): PADDING = 2 # per column if self.config.table_width_mode == 'explicit': # target width INCLUDES padding and column marks | - target_width = self.config.max_table_width - (PADDING + 1) * n_col - 1 - logger.info(f'Col padding effect {self.config.max_table_width=} ==> {target_width=}') + target_width = self.config.max_table_width - \ + (PADDING + 1) * n_col - 1 + logger.info(f'Col padding effect { + self.config.max_table_width=} ==> {target_width=}') elif self.config.table_width_mode == 'natural': target_width = natural + (PADDING + 1) * n_col + 1 elif self.config.table_width_mode == 'breakable': @@ -936,7 +940,8 @@ class GT(object): # extra space for the headers to relax, if useful if self.config.table_width_header_adjust > 0: - max_extra = int(self.config.table_width_header_adjust * target_width) + max_extra = int( + self.config.table_width_header_adjust * target_width) else: max_extra = 0 @@ -1004,7 +1009,14 @@ class GT(object): ans['recommended'], ans['natural_w_header']) # Ensure final constraint - ans['recommended'] = ans['recommended'].astype(int) + try: + ans['recommended'] = ans['recommended'].astype(int) + except IntCastingNaNError: + print('getting error') + print(ans['recommended']) + ans['recommended'] = pd.to_numeric( + ans['recommended'], errors='coerce').fillna(0).astype(int) + logger.info("Raw rec: %s\tTweaks: %s\tActual: %s\tTarget: %s\tOver/(U): %s", ans['raw_rec'].sum(), ans['header_tweak'].sum(), @@ -1517,7 +1529,7 @@ class GT(object): font-weight: bold; }} '''] - for i, w in enumerate(config.tabs): + for i, w in enumerate(tabs): style.append(f' #{self.df_id} .grt-c-{i} {{ width: {w}em; }}') style.append('') logger.info('CREATED CSS') @@ -1547,15 +1559,15 @@ class GT(object): colw, tabs = GT.estimate_column_widths( self.df, self.config.max_table_width, nc_index=self.nindex, scale=1, equal=self.config.equal) if self.config.debug: - print(f'Make html Input {self.config.tabs=}\nComputed {tabs=}') - if self.config.tabs is not None: - if len(tabs) == len(self.config.tabs): - tabs = self.config.tabs - elif len(self.config.tabs) == 1: - tabs = self.config.tabs * len(tabs) + print(f'Make html Input {self.tabs=}\nComputed {tabs=}') + if self.tabs is not None: + if len(tabs) == len(self.tabs): + tabs = self.tabs + elif len(self.tabs) == 1: + tabs = self.tabs * len(tabs) else: logger.error( - f'{self.config.tabs=} must be None, a single number, or a list of numbers of the correct length. Ignoring.') + f'{self.tabs=} must be None, a single number, or a list of numbers of the correct length. Ignoring.') # print('HTML ' + ', '.join([f'{c:,.2f}' for c in tabs])) # set column widths; tabs returns lengths of strings in each column @@ -1665,7 +1677,9 @@ class GT(object): # dx = data in index # if this is the level that changes for this row # will use a top rule hence omit i = 0 which already has an hrule - if i > 0 and hrule == '' and j == index_change_level[i]: + # appears in the index change level. But if it DOES NOT appear then + # it isn't a change level so no rule required + if i > 0 and hrule == '' and i in index_change_level and j == index_change_level[i]: hrule = f'grt-hrule-{j}' # html.append(f'{c}') col_id = f'grt-c-{j}' @@ -1752,8 +1766,12 @@ class GT(object): @staticmethod def apply_formatters_work(df, formatters): """Apply formatters to a DataFrame.""" - new_df = pd.DataFrame({i: map(f, df.iloc[:, i]) - for i, f in enumerate(formatters)}) + try: + new_df = pd.DataFrame({i: map(f, df.iloc[:, i]) + for i, f in enumerate(formatters)}) + except TypeError: + print('NASTY TYPE ERROR') + raise new_df.columns = df.columns return new_df @@ -1899,7 +1917,7 @@ class GT(object): row sep={row_sep}em, column sep={column_sep}em, nodes in empty cells, - nodes={{rectangle, scale={scale}, text badly ragged {config.debug}}}, + nodes={{rectangle, scale={scale}, text badly ragged {debug}}}, """ # put draw=blue!10 or so in nodes to see the node @@ -1928,12 +1946,12 @@ class GT(object): "ignore", category=pd.errors.PerformanceWarning) df = df.reset_index( drop=False, col_level=df.columns.nlevels - 1) - if config.sparsify: + if sparsify: if hrule is None: hrule = set() - for i in range(config.sparsify): - # TODO update to new config.sparsify!! - df.iloc[:, i], rules = GT.config.sparsify_old(df.iloc[:, i]) + for i in range(sparsify): + # TODO update to new sparsify!! + df.iloc[:, i], rules = GT.sparsify_old(df.iloc[:, i]) # don't want lines everywhere if len(rules) < len(df) - 1: hrule = set(hrule).union(rules) @@ -1960,15 +1978,15 @@ class GT(object): # estimate... originally called guess_column_widths, with more parameters colw, tabs = GT.estimate_column_widths(df, self.config.max_table_width, nc_index=nc_index, scale=self.config.tikz_scale, equal=self.config.equal) # noqa if self.config.debug: - print(f'Make TikZ Input {self.config.tabs=}\nComputed {tabs=}') - if self.config.tabs is not None: - if len(tabs) == len(self.config.tabs): - tabs = self.config.tabs - elif len(self.config.tabs) == 1: - tabs = self.config.tabs * len(tabs) + print(f'Make TikZ Input {self.tabs=}\nComputed {tabs=}') + if self.tabs is not None: + if len(tabs) == len(self.tabs): + tabs = self.tabs + elif len(self.tabs) == 1: + tabs = self.tabs * len(tabs) else: logger.error( - f'{self.config.tabs=} must be None, a single number, or a list of numbers of the correct length. Ignoring.') + f'{self.tabs=} must be None, a single number, or a list of numbers of the correct length. Ignoring.') # print('TIKZ ' + ', '.join([f'{c:,.2f}' for c in tabs])) # print(f'TIKZ {colw=}, {tabs=}') logger.info(f'tabs: {tabs}') @@ -1995,10 +2013,12 @@ class GT(object): latex = '' else: latex = f'[{latex}]' - config.debug = '' + debug = '' if self.config.debug: # color all boxes - config.debug = ', draw=blue!10' + debug = ', draw=blue!10' + else: + debug = '' sio.write(header.format(container_env=container_env, caption=caption, extra_defs=extra_defs, @@ -2006,7 +2026,7 @@ class GT(object): column_sep=column_sep, row_sep=row_sep, latex=latex, - debug=self.config.debug)) + debug=debug)) # table header # title rows, start with the empty spacer row @@ -2024,7 +2044,8 @@ class GT(object): if i == 1: # first column sets row height for entire row sio.write(f'\tcolumn {i:>2d}/.style={{' - f'nodes={{align={ad[al]:<6s}}}, text height=0.9em, text depth=0.2em, ' + f'nodes={{align={ + ad[al]:<6s}}}, text height=0.9em, text depth=0.2em, ' f'inner xsep={column_sep}em, inner ysep=0, ' f'text width={max(2, 0.6 * w):.2f}em}},\n') else: @@ -2053,7 +2074,7 @@ class GT(object): if isinstance(df.columns, pd.MultiIndex): for lvl in range(len(df.columns.levels)): nl = '' - sparse_columns[lvl], mi_vrules[lvl] = GT.config.sparsify_mi(df.columns.get_level_values(lvl), + sparse_columns[lvl], mi_vrules[lvl] = GT.sparsify_mi(df.columns.get_level_values(lvl), lvl == len(df.columns.levels) - 1) for cn, c, al in zip(df.columns, sparse_columns[lvl], align): # c = wfloat_format(c) @@ -2268,7 +2289,7 @@ class GT(object): # data all seems about the same width tabs.append(common_size) logger.info(f'Determined tab config.spacing: {tabs}') - if config.equal: + if equal: # see if config.equal widths makes sense dt = tabs[nl:] if max(dt) / sum(dt) < 4 / 3: @@ -2302,7 +2323,7 @@ class GT(object): @staticmethod def sparsify_old(col): """ - config.sparsify col values, col a pd.Series or dict, with items and accessor + sparsify col values, col a pd.Series or dict, with items and accessor column results from a reset_index so has index 0,1,2... this is relied upon. TODO: this doesn't work if there is a change in a higher level but not this level """ diff --git a/greater_tables/gtformats.py b/greater_tables/gtformats.py index cca9448..532827b 100644 --- a/greater_tables/gtformats.py +++ b/greater_tables/gtformats.py @@ -1,3 +1,4 @@ +# coding: utf-8 """ Define text table formats. @@ -80,3 +81,11 @@ GT_Format = TableFormat( # padding=1, # with_header_hide=None # ) + + +def default_formatter(x): + """ + + + + """ diff --git a/greater_tables/testdf.py b/greater_tables/testdf.py index be8acdb..a41657f 100644 --- a/greater_tables/testdf.py +++ b/greater_tables/testdf.py @@ -4,262 +4,226 @@ Make fake dataframes for testing. GPT from SJMM design. """ -# from pathlib import Path -# from dataclasses import dataclass, field -# from typing import Optional, Union -# from datetime import datetime, timedelta -# import hashlib -# import re - - -# import numpy as np -# import pandas as pd -# from faker import Faker - - -# @dataclass -# class TestDataFrameFactory: -# """ -# Factory for generating small synthetic pandas DataFrames for testing. - -# Attributes: -# colname_words: Optional list of strings to use for column names. -# default_word_count: Max number of words for string columns (default 3). -# seed: Optional random seed. If None, one is generated. -# """ -# colname_words: Optional[list[str]] = None -# default_word_count: int = 3 -# seed: Optional[int] = None -# _last_args: dict = field(default_factory=dict, init=False) - -# def __post_init__(self): -# self.faker = Faker() -# self.seed = int(self.seed if self.seed is not None else np.random.SeedSequence().entropy) -# self.rng = np.random.default_rng(self.seed) - -# def make(self, rows: int, columns: Union[int, str], index: Union[int, str] = 0, -# col_index: Union[int, str] = 0, missing: float = 0.0) -> pd.DataFrame: -# """ -# Generate a test DataFrame with the given specification. - -# Args: -# rows: Number of rows. -# columns: Column type spec (int for all float cols, or string type codes). -# index: Index level types (int for RangeIndex or string like 'ti'). -# col_index: Column index levels (same format as `index`). -# missing: Proportion of missing data in each column. - -# Returns: -# DataFrame -# """ -# self._last_args = dict(rows=rows, columns=columns, index=index, col_index=col_index, missing=missing) -# return self._generate(**self._last_args) - -# def another(self, new_seed: bool = True) -> pd.DataFrame: -# """ -# Generate another DataFrame with the last parameters. - -# Args: -# new_seed: If True, re-randomize the generator seed. - -# Returns: -# DataFrame -# """ -# if new_seed: -# self.seed = int(np.random.SeedSequence().entropy) -# self.rng = np.random.default_rng(self.seed) -# return self._generate(**self._last_args) - -# def random(self, index_levels: int = 1, column_levels: int = 1) -> pd.DataFrame: -# """ -# Generate a DataFrame with randomly chosen settings. - -# Args: -# index_levels: Number of index levels to use. -# column_levels: Number of column MultiIndex levels. - -# Returns: -# DataFrame -# """ -# rows = self.rng.integers(10, 50) -# col_types = self.rng.choice(['d', 'f', 'i', 's1', 's3', 's7', 'h', 't', 'p'], size=self.rng.integers(3, 7)) -# missing = round(float(self.rng.uniform(0, 0.15)), 2) -# index = ''.join(self.rng.choice(['t', 'd', 'i', 's2'], size=index_levels)) -# col_index = ''.join(self.rng.choice(['s', 'i', 'd'], size=column_levels)) -# return self.make(rows=rows, columns=''.join(col_types), index=index, col_index=col_index, missing=missing) - -# def _parse_colspec(self, spec: str) -> list[str]: -# return re.findall(r's\d+|[a-z]', spec) - - -# def _generate(self, rows: int, columns: Union[int, str], index: Union[int, str], -# col_index: Union[int, str], missing: float) -> pd.DataFrame: -# if isinstance(columns, int): -# col_types = ['s3'] * columns -# else: -# col_types = self._parse_colspec(columns) - -# colnames = self._make_column_names(len(col_types)) -# data = { -# name: self._generate_column(dt, rows) for name, dt in zip(colnames, col_types) -# } -# df = pd.DataFrame(data) -# df.index = self._make_index(index, rows, "i") -# df.columns = self._make_index(col_index, len(df.columns), "c") if isinstance(col_index, str) else df.columns -# df = self._insert_missing(df, missing) -# return df - -# def _make_column_names(self, n: int) -> list[str]: -# if self.colname_words: -# pool = self.colname_words -# else: -# pool = [self.faker.word() for _ in range(n * 2)] -# names = [] -# used = set() -# for word in pool: -# if len(names) >= n: -# break -# if word not in used: -# names.append(word) -# used.add(word) -# while len(names) < n: -# names.append(f"col_{len(names)}") -# return names - -# def _generate_column(self, dtype: str, n: int) -> pd.Series: -# if dtype.startswith('s'): -# max_words = int(dtype[1:]) if len(dtype) > 1 else self.default_word_count -# return pd.Series([" ".join(self.faker.words(self.rng.integers(max_words // 2 + 1, max_words + 1))) for _ in range(n)]) -# if dtype == 'f': -# return pd.Series(self.rng.normal(loc=100, scale=25, size=n)) -# if dtype == 'i': -# return pd.Series(self.rng.integers(1e9, 1e12, size=n), dtype='int64') -# if dtype == 'd': -# start_date = self.faker.date_between(start_date='-10y', end_date='today') -# return pd.Series(pd.date_range(start=start_date, periods=n, freq='D')) -# if dtype == 't': -# start_dt = datetime.now() - timedelta(days=365 * 2) -# return pd.Series([start_dt + timedelta(minutes=int(self.rng.integers(0, 2 * 365 * 24 * 60))) for _ in range(n)]) -# if dtype == 'h': -# return pd.Series([ -# hashlib.blake2b(f"val{i}".encode(), digest_size=32).hexdigest() -# for i in range(n) -# ]) -# if dtype == 'p': -# return pd.Series([str(Path(f"/data/{self.faker.word()}/{i}.dat")) for i in range(n)]) -# raise ValueError(f"Unknown dtype: {dtype}") - -# def _make_index(self, desc: Union[int, str], n: int, label_prefix: str) -> pd.Index: -# if isinstance(desc, int): -# return pd.RangeIndex(n, name=f"{label_prefix}0") -# levels = [] -# names = [] -# for j, dt in enumerate(desc): -# s = self._generate_column(dt, n) -# levels.append(s) -# names.append(f"{label_prefix}{j}") -# return pd.MultiIndex.from_arrays(levels, names=names) - -# def _insert_missing(self, df: pd.DataFrame, prop: float) -> pd.DataFrame: -# if prop <= 0: -# return df -# n_rows = df.shape[0] -# for col in df.columns: -# n_missing = max(1, int(np.floor(prop * n_rows))) -# missing_indices = self.rng.choice(n_rows, size=n_missing, replace=False) -# df.iloc[missing_indices, df.columns.get_loc(col)] = np.nan -# return df - - -# Reimport necessary modules after kernel reset -from pathlib import Path -from dataclasses import dataclass, field -from typing import Optional, Union from datetime import datetime, timedelta +from itertools import cycle +from math import prod +from pathlib import Path +from typing import Optional, Union import hashlib -import numpy as np -import pandas as pd -from faker import Faker +import random import re -@dataclass -class TestDataFrameFactory: - colname_words: Optional[list[str]] = None - default_word_count: int = 3 - seed: Optional[int] = None - _last_args: dict = field(default_factory=dict, init=False) +import numpy as np +import pandas as pd - def __post_init__(self): - self.faker = Faker() - self.seed = int(self.seed if self.seed is not None else np.random.SeedSequence().entropy) + +name_word_list = [ + "account", + "address", + "amount", + "balance", + "category", + "client", + "combined ratio", + "comment", + "currency", + "description", + "duration", + "email", + "entry", + "estimate", + "extension", + "failure", + "filename", + "identifier", + "location", + "loss ratio", + "note", + "operation", + "premium", + "processing", + "project", + "reference", + "remark", + "status", + "supplier", + "timestamp", + "transaction", + "type", + "user", + 'expense ratio', + 'loss date' +] + + +class TestDataFrameFactory: + """ + Create super-dooper test dataframes. + """ + + def __init__(self, seed: Optional[int] = None): + """ + Factory for generating small synthetic pandas DataFrames for testing. + + Attributes: + seed: Optional random seed. If None, one is generated. + """ + self._last_args = {} + self.seed = int( + seed if seed is not None else np.random.SeedSequence().entropy) + + # rng self.rng = np.random.default_rng(self.seed) + # word list for names of index levels + nwl = name_word_list[:] + random.shuffle(nwl) + self._index_namer = cycle(nwl) + + # read words and create cycler + p = Path(__file__).parent / 'words-12.md' + assert p.exists() + txt = p.read_text(encoding='utf-8') + word_list = txt.split('\n') + temp = word_list[:] + random.shuffle(temp) + self._word_gen = cycle(temp) + + # read tex expressions and create cycler + tex_list = pd.read_csv(Path(__file__).parent / + 'tex_list.csv')['expr'].to_list() + tex_list = [i for i in tex_list if len(i) < 50] + random.shuffle(tex_list) + self._tex_gen = cycle(tex_list) + + # lengths of index (word count) sampled from: + self.index_value_lengths = [1]*10 + [2] * 4 + [3] + def make(self, rows: int, columns: Union[int, str], index: Union[int, str] = 0, col_index: Union[int, str] = 0, missing: float = 0.0) -> pd.DataFrame: - self._last_args = dict(rows=rows, columns=columns, index=index, col_index=col_index, missing=missing) - return self._generate(**self._last_args).sort_index() + """ + Generate a test DataFrame with the given specification. + + Data types + + d date + f float + h hash + i integer + l log float (greater range than float) + m year - month + p path (filename) + sx string length x + t time + x tex text - an equation + y year + + + Args: + rows: Number of rows. + columns: Column type spec (int for all float cols, or string type codes). + index: Index level types (int for RangeIndex or string like 'ti'). + col_index: Column index levels (same format as `index`). + missing: Proportion of missing data in each column. + + Returns: + DataFrame + """ + self._last_args = dict(rows=rows, columns=columns, + index=index, col_index=col_index, missing=missing) + return self._generate(**self._last_args) def another(self, new_seed: bool = True) -> pd.DataFrame: + """ + Generate another DataFrame with the last parameters. + + Args: + new_seed: If True, re-randomize the generator seed. + + Returns: + DataFrame + """ if new_seed: self.seed = int(np.random.SeedSequence().entropy) self.rng = np.random.default_rng(self.seed) - return self._generate(**self._last_args).sort_index() + return self._generate(**self._last_args) - def random(self, index_levels: int = 1, column_levels: int = 1) -> pd.DataFrame: - rows = self.rng.integers(10, 50) - col_types = self.rng.choice(['d', 'f', 'i', 's3', 'h', 't', 'p'], size=self.rng.integers(3, 7)) + def random(self, index_levels: int = 0, column_levels: int = 0) -> pd.DataFrame: + """ + Generate a DataFrame with randomly chosen settings. + + Args: + index_levels: Number of index levels to use. + column_levels: Number of column MultiIndex levels. + + Returns: + DataFrame + """ + if index_levels == 0: + index_levels = random.choice([1, 1, 1, 1, 1, 2, 2, 3]) + if column_levels == 0: + column_levels = random.choice([1, 1, 1, 1, 1, 2, 2, 3]) + rows = self.rng.integers(5 * index_levels, 10 * index_levels) + col_types = self.rng.choice( + ['d', 'f', 'i', 's3', 'l', 'h', 't', 'p'], size=self.rng.integers(3, 7)) missing = round(float(self.rng.uniform(0, 0.15)), 2) - index = ''.join(self.rng.choice(['t', 'd', 'i', 's2'], size=index_levels)) - col_index = ''.join(self.rng.choice(['s', 'i', 'd'], size=column_levels)) + index = ''.join(self.rng.choice( + ['t', 'd', 'i', 's2'], size=index_levels)) + col_index = ''.join(self.rng.choice( + ['s', 's2', 's2', 's3'], size=column_levels)) return self.make(rows=rows, columns=''.join(col_types), index=index, col_index=col_index, missing=missing) def _generate(self, rows: int, columns: Union[int, str], index: Union[int, str], col_index: Union[int, str], missing: float) -> pd.DataFrame: - col_types = ['f'] * columns if isinstance(columns, int) else self._parse_colspec(columns) - colnames = self._make_column_names(len(col_types)) - data = { - name: self._generate_column(dt, rows) for name, dt in zip(colnames, col_types) - } - df = pd.DataFrame(data) - df.index = self._make_index(index, rows, "i") - df.columns = self._make_index(col_index, len(df.columns), "c") if isinstance(col_index, str) else df.columns + # if columns is an int then make up types + if isinstance(columns, int): + col_types = self.rng.choice( + ['d', 't', 'f', 'l', 'i', 's1', 's3', 's9', 'h', 'p', 'x'], size=columns) + else: + col_types = self._parse_colspec(columns) + # if col_index is an int then use all strings of that depth + if isinstance(col_index, int): + col_index_types = ['s'] * col_index + else: + col_index_types = self._parse_colspec(col_index) + if isinstance(index, int): + index = ['s'] * index + else: + index = self._parse_colspec(index) + print(index) + # col names are a transposed index. + df = pd.DataFrame(index=range(rows)) + col_idx = self._make_index(col_index_types, len(col_types)) + for dt, c in zip(col_types, range(len(col_idx))): + df[c] = self._generate_column(dt, rows) + df.columns = col_idx + df.index = self._make_index(index, rows) df = self._insert_missing(df, missing) return df def _parse_colspec(self, spec: str) -> list[str]: return re.findall(r's\d+|[a-z]', spec) - def _make_column_names(self, n: int) -> list[str]: - if self.colname_words: - pool = self.colname_words - else: - pool = [self.faker.word() for _ in range(n * 2)] - names, used = [], set() - for word in pool: - if len(names) >= n: - break - if word not in used: - names.append(word) - used.add(word) - while len(names) < n: - names.append(f"col_{len(names)}") - return names - def _generate_column(self, dtype: str, n: int) -> pd.Series: if dtype.startswith('s'): - max_words = int(dtype[1:]) if len(dtype) > 1 else self.default_word_count - return pd.Series([" ".join(self.faker.words(self.rng.integers(1, max_words + 1))) for _ in range(n)]) + max_words = int(dtype[1:]) if len(dtype) > 1 else 1 + return pd.Series([" ".join(self.word() for i in range(max_words)) for j in range(n)]) if dtype == 'f': - return pd.Series(self.rng.normal(loc=100, scale=25, size=n)) + return pd.Series(self.rng.normal(loc=100000, scale=250000, size=n)) + if dtype == 'l': + # log float (greater range) + return pd.Series(np.exp(self.rng.normal(loc=-4 / 2 + 4, scale=4, size=n))) if dtype == 'i': - return pd.Series(self.rng.integers(1e9, 1e12, size=n), dtype='int64') + return pd.Series(self.rng.integers(-1e4, 1e6, size=n), dtype='int64') if dtype == 'd': - start_date = self.faker.date_between(start_date='-10y', end_date='today') + start_date = TestDataFrameFactory.random_date_within_last_n_years( + 10) return pd.Series(pd.date_range(start=start_date, periods=n, freq='D')) if dtype == 't': start_dt = datetime.now() - timedelta(days=365 * 2) return pd.Series([ - start_dt + timedelta(minutes=int(self.rng.integers(0, 2 * 365 * 24 * 60))) + start_dt + + timedelta(minutes=int(self.rng.integers(0, 2 * 365 * 24 * 60))) for _ in range(n) ]) if dtype == 'h': @@ -268,45 +232,122 @@ class TestDataFrameFactory: for i in range(n) ]) if dtype == 'p': - return pd.Series([str(Path(f"/data/{self.faker.word()}/{i}.dat")) for i in range(n)]) + return pd.Series([str(Path(f"/data/{self.word()}/{i}.dat")) for i in range(n)]) + if dtype == 'x': + # tex + return pd.Series([self.tex() for i in range(n)]) raise ValueError(f"Unknown dtype: {dtype}") - def _make_index(self, desc: Union[int, str], n: int, label_prefix: str) -> pd.Index: + def _make_index(self, desc: Union[int, str, list[str]], n: int) -> pd.Index: if isinstance(desc, int): - return pd.RangeIndex(n, name=f"{label_prefix}0") + return pd.RangeIndex(n, name=self.index_name()) + if isinstance(desc, str): + desc = self._parse_colspec(desc) if len(desc) == 1: - s = self._generate_column(desc[0], n) - return pd.Index(s, name=f"{label_prefix}0") - return self._make_hierarchical_index(desc, n, label_prefix) + if desc[0] == 'i': + return pd.RangeIndex(n, name=self.index_name()) + elif desc[0] in ('d', 't', 'x'): + vals = self._generate_column(desc[0], n) + return pd.Index(vals, name=self.index_name()) + elif not all(i[0] == 's' for i in desc): + raise ValueError( + f'Inadmissible index spec: only string, int, and date types allowed, not {desc}.') + level_value_lengths = [1 if len(i) == 1 else int(i[1:]) for i in desc] + return self.make_index(rows=n, levels=len(desc), level_value_lengths=level_value_lengths, + p0=1, padding=2) - def _make_hierarchical_index(self, desc: str, n: int, label_prefix: str) -> pd.MultiIndex: - """ - Generate a nested hierarchical index of length `n` with `len(desc)` levels. - Levels are naturally nested, i.e., upper levels have fewer unique values. - """ - levels = [] + def index_name(self): + """Return a one-word index name.""" + return next(self._index_namer) - # generate lower-level (more detailed) values with full cardinality - detailed = self._generate_column(desc[-1], n) - levels.insert(0, detailed) + def word(self): + """Return a random word (cycles eventually).""" + return next(self._word_gen) - # generate higher levels with fewer unique values - for i, dt in enumerate(desc[:-1]): - u = 2 if i == 0 else 3 - unique_vals = self._generate_column(dt, u).unique() - repeated = self.rng.choice(unique_vals, size=n, replace=True) - levels.insert(0, repeated) - - names = [f"{label_prefix}{j}" for j in range(len(desc))] - return pd.MultiIndex.from_arrays(levels, names=names) + def tex(self): + """Return a blob of TeX.""" + return next(self._tex_gen) + @staticmethod + def random_date_within_last_n_years(n: int) -> pd.Timestamp: + today = datetime.today() + days = random.randint(0, n * 365) + return pd.Timestamp(today - timedelta(days=days)) def _insert_missing(self, df: pd.DataFrame, prop: float) -> pd.DataFrame: + """Insert missing values into dataframe.""" if prop <= 0: return df n_rows = df.shape[0] for col in df.columns: n_missing = max(1, int(np.floor(prop * n_rows))) - missing_indices = self.rng.choice(n_rows, size=n_missing, replace=False) + missing_indices = self.rng.choice( + n_rows, size=n_missing, replace=False) df.iloc[missing_indices, df.columns.get_loc(col)] = np.nan return df + + @staticmethod + def _is_prime(p: int) -> bool: + if p < 2: + return False + if p == 2: + return True + if p % 2 == 0: + return False + for i in range(3, int(p**0.5) + 1, 2): + if p % i == 0: + return False + return True + + @staticmethod + def _next_prime(p: int) -> int: + if p < 2: + return 2 + p += 1 if p % 2 == 0 else 2 # ensure odd start > p + while True: + if TestDataFrameFactory._is_prime(p): + return p + p += 2 + + @staticmethod + def primes_for_product(n: int, v: int, p0: int) -> list[int]: + """Return a list of distinct primes all >= p0 whose product is >= n.""" + primes = [] + p = TestDataFrameFactory._next_prime(max(p0 - 1, 1)) + while len(primes) < v: + primes.append(p) + p = TestDataFrameFactory._next_prime(p) + + while prod(primes := sorted(primes)) < n: + # increase one level until product is high enough + p = TestDataFrameFactory._next_prime(primes[-1]) + primes[-1] = p + # shuffle order + random.shuffle(primes) + return primes + + def make_index(self, rows: int, levels: int, + level_value_lengths: Union[list[int], None] = None, + p0: int = 1, + padding: int = 2): + """ + Make an Index with unique values, rows x len(level_value_lengths) cols. + + level_velue_lengths shows how many words long each value should be. + padding = over-sample by padding and select sample. + """ + if level_value_lengths is None: + level_value_lengths = random.sample( + self.index_value_lengths, levels) + else: + assert levels == len( + level_value_lengths), 'levels must equal len(level_value_lengths)' + level_choices = self.primes_for_product(rows * padding, levels, p0=p0) + r = [cycle([' '.join([self.word() for _ in range(w)]) for _ in range(k)]) + for w, k in zip(level_value_lengths, level_choices)] + x = [[next(j) for j in r] for i in range(rows)] + names = random.sample(name_word_list, levels) + idx = pd.MultiIndex.from_tuples( + random.sample(x, rows), names=names).sort_values() + assert idx.is_unique + return idx diff --git a/greater_tables/tex_list.csv b/greater_tables/tex_list.csv new file mode 100644 index 0000000..2c5365c --- /dev/null +++ b/greater_tables/tex_list.csv @@ -0,0 +1,5804 @@ +,expr +0,$\bar M$ +1,$m(1)=m_3=0$ +2,$X_2=2$ +3,$a=1$ +4,$\mathbf{M_{1}\Delta X}$ +5,$U < s$ +6,$n \le pN < (n+1)$ +7,"$\mathsf{TI,\ MON}$" +8,$\log(g')$ +9,$(.*?)\$ +10,$\rho(X)=\infty$ +11,$F(x-) = \lim_{t\uparrow x} F(t)$ +12,"$\mathsf{MON,\ TI,\ PH}$" +13,$\mathsf E_Q\left[\dfrac{X_i}{X}(X\wedge A)\right] + \delta A \mathsf E_Q[X_i/X\mid X > a]$ +14,$Y\succeq Z$ +15,$|S|$ +16,$\mathsf{CONVEX}$ +17,$\Pr(X < x)\le \Pr(X\le x)$ +18,$\mathsf E_{\mathsf Q}[\kappa_i(X)]$ +19,$s^{1/2}$ +20,$1000e^{\mu}$ +21,$p^* =0.7501$ +22,$X=\sum_j X_j$ +23,$\beta_{2}$ +24,$\sigma=0.50$ +25,$Z(s)=\Phi^{-1}(s)$ +26,$\hat p=1-g^{-1}(1-p)$ +27,$\sigma^2 t$ +28,$\uparrow\uparrow$ +29,$F(x)=1-e^{-x/\mu}$ +30,$g(S(X))$ +31,$0<\rho\le 1$ +32,$\bar Q_{0}=a_{0}-\bar P_{0}$ +33,$s\downarrow 0$ +34,$X=\frac{1}{n}\sum_i X_i$ +35,$>(s_0/2^{n+1})2^n\bar q(s_0)=s_0\bar q(s_0)/2$ +36,$\mathsf E_Q[X]$ +37,$\rho(X)>\max(X) g(0+)=\infty$ +38,$\lambda\to\infty$ +39,$\mathsf{j}(a)=6$ +40,"$g(s)=w+(1-w)s, s>0$" +41,$\mathsf{TVaR}_{0.65}$ +42,$\Pr(X = q(p)) > 0$ +43,$c(S\cup\{i\})=c(S)+c(i)$ +44,$\mu(\{p_j\})$ +45,$q(Y)$ +46,$Z_A$ +47,$\mathcal D(X)\ge 0$ +48,$p=\text{Pr}[L^* > A]$ +49,$X_{t+dt}=X_t + \mu dt + \sigma dW_{dt}$ +50,$\mathsf E[X] + \pi\mathsf E[(X-\mathsf E X)^+]$ +51,$u(x)=-v(-x)$ +52,$g(x)=1$ +53,$F_{\mathbf{v}}(x)=s$ +54,${n}-X_2$ +55,$U_X > p$ +56,$b_i$ +57,$\rho(\nu Z) \le \nu\rho(Z)$ +58,$\Phi(x):=\int_{-\infty}^x \phi(t)dt$ +59,$\rho(U)=\mathsf E_\mathsf Q[U]$ +60,$U = A$ +61,$X\le l$ +62,$U_X < p$ +63,$g'(1-p) \frac{q\wedge \alpha}{q}$ +64,$rpq$ +65,$c>0$ +66,$Y=0$ +67,$1-p_0$ +68,"$(p, 1-g^{-1}(1-p))=(p,\hat p)$" +69,$\mathit{MV}(a)$ +70,$Z_4$ +71,"$\kappa_i(\mathbf{v}, x)$" +72,"$x=A,L,S$" +73,$c(S)=\rho(\sum_{i\in S} X_i)$ +74,$F:\mathbb{R}^n \to \XXX$ +75,$S_X(a)$ +76,$\mathsf E[X\mid t]$ +77,"$a,b=\pm 1/n$" +78,"$x_{1,i}, x_{2,i}$" +79,$1_{X>a}$ +80,"$\int_0^\infty -z(x)\,dF(x)=-1$" +81,$k\mapsto k\rho(X)$ +82,$\rho_g(X)=\mu+\lambda\sigma$ +83,$\hat q$ +84,$F_X^{-1}(V)=q_X(V)$ +85,$Y=\mathsf E[Z\mid\mathcal G]$ +86,$0\le\beta<1$ +87,$p>S(x^*)$ +88,$a\le X\le b$ +89,$P(x)=A(1_{X>x})=g(S(x))$ +90,$g(S)\Delta X'$ +91,$1<\lambda=k+f$ +92,$1./16=0.0625$ +93,"$\alpha>1,0\le\beta\le 1$" +94,$P=(1+r)\lambda\mathsf E[X]$ +95,$g''(s)\le 0$ +96,$S(x_{max})=0$ +97,$\{X=x\}$ +98,$\mathsf{TVaR}_p(X)=\TCE_p(X)=\mathsf E[X\mid X \ge \mathsf{VaR}_p(X)]$ +99,$\rho_g(X\wedge a)$ +100,$x\mathsf E[X_i/X\mid X>x]$ +101,$Z=(1-p)^{-1}1_{\tilde X>q_{\tilde X}(p)}$ +102,$\mathsf E_\mathsf{Q_r}[X_j]$ +103,$G(x)=\mathbb{Q}(\{\omega\mid X(\omega)\le x\})$ +104,"$X_{t-1,1}$" +105,$Z_1$ +106,"$X_{t,3}$" +107,$X_2(10)$ +108,$\mathsf E[X_1]=\mu$ +109,$X\le x$ +110,$r = (g(s)-s)/(1-g(s))$ +111,$\mathsf{TVaR}_1(X)$ +112,$\rho(Y)=\rho(X)g(p)=g(q)g(p).$ +113,$\mathbf{s_0}$ +114,$M(x)=g(S(x))-S(x)$ +115,$Y_{1}$ +116,$g(s)-s$ +117,$-U$ +118,$X_n(\omega)\to X(\omega)$ +119,$^{***}$ +120,$\bar S(a)$ +121,$\sum (X\wedge a)p$ +122,"$\{1,2,\dots, N\}$" +123,$D\rho_{X_g}(X_c)$ +124,$\mathbf s$ +125,$(g(s)-s)/(1-g(s))=\iota$ +126,"$P_X(a,b] = F(b)-F(a)$" +127,$k > 0$ +128,$\mathsf EPD_p(X)$ +129,$X_n\downarrow X$ +130,$\mathsf E[X\mid X>x]/\Pr(X>x)$ +131,$x\to \infty$ +132,$\Phi(Z(s))=s$ +133,$q^-(p) = \inf\ \{ x\mid F(x) \ge p\}$ +134,$Y(\omega_1)\le Y(\omega_2)$ +135,$v(A)\le v(B)$ +136,$\alpha_i(a) S(a)$ +137,$\ge \mathsf E[X]$ +138,$\hat{\tilde p}=1-g^{-1}(1-[1-g(1-p)])=p$ +139,$\pi(X)=\log(m_X(\alpha)) / \alpha$ +140,$E[s|W=t]$ +141,$S(x)\gg 0$ +142,$1-\beta_i(x)g(S(x))$ +143,$\mathsf E[X_i\mid X=q(p)]$ +144,$S_X(x)=\Phi(-(x-\mu)/\sigma)$ +145,$\pi(X) = \rho(X\wedge \alpha(X))$ +146,$a(\mathbf{v}) =\mathsf{VaR}_p(X(\mathbf{v}))= q_{\mathbf{v}}(p)$ +147,$\mathsf Q \in \mathcal Q$ +148,$a=D+S$ +149,"$\bar P_{t,0}$" +150,"$0, 8, 10$" +151,$Q(x)/(1-S(x))$ +152,$p=1/6$ +153,$\rho=\mathsf{TVaR}_{0.95}$ +154,$\mathsf E_{\mathsf Q}[X\mid \mathcal F]=\mathsf E[XZ\mid \mathcal F]/\mathsf E[Z\mid \mathcal F]$ +155,$f(S_t)=\log(S_t)$ +156,$\int_0^\infty xdF(x) =\int_0^\infty xf(x)dx$ +157,$u_j(x)$ +158,$f_{xx}=-1/S_t^2$ +159,$X$ +160,$t+2$ +161,$n\ge m$ +162,"$\{1+\lambda(f-\mathsf E f) \mid f\ge 0, \|f\|_q\le 1 \}$" +163,$|f|$ +164,$b$ +165,$g'(S(x))$ +166,$r_l$ +167,"$\rho(Y_{2,0})$" +168,$1+\iota^*=(1+\iota)(1+\tau)$ +169,$r_f/(1+r_f)$ +170,$L^r$ +171,$u(0)=0$ +172,$(ng)$ +173,$E[X|X>qp]$ +174,$\mathbf{S\Delta X'}$ +175,$1-g(S)$ +176,$a_{0}$ +177,$\rho_g(X \wedge a)$ +178,$\rho(0)=\rho(0 \times X)=0\times \rho(X)=0$ +179,$-\rho(-X)\le \mathsf E[X]$ +180,$\rho_g(X)$ +181,"$n={{n}}, p=1/{{p}}={{pf}}$" +182,$\mathsf E[Xe^{hX}]/\mathsf E[e^{hX}]$ +183,$\Delta Q_{gc}(a) = a_{gc}-P(X_{0}(a_{gc}))-a$ +184,"$\bar S_i = \sum_{j} X_{i,j}p_j$" +185,$\mathcal G\subset\mathcal F$ +186,$10^{-12}$ +187,"$x\in[0,\infty)$" +188,$F_0 = \bar P_{act}-\bar P = R-\bar M$ +189,$X_{-3}$ +190,$\bar\delta$ +191,$t>0$ +192,$\mathit{LGD}$ +193,$\mu_c$ +194,$\mathsf E_{\mathsf Q}[X]=\mathsf E[XZ]$ +195,$p<0.5$ +196,$a_h=2-a_l<2-b_l=b_h$ +197,"$F(p)=\mu([0,p])$" +198,$\lambda dt\to 0$ +199,$0 < p_0 < p_1 < 1$ +200,$p\mapsto g'(1-p)$ +201,$\omega=0.\omega_1\omega_2\dots$ +202,$BCD$ +203,$\beta_i(x)<\alpha_i(x)$ +204,$\nu=\nu(p)$ +205,$a_1 = a(Y_{1})$ +206,$\mathit{NPV}_{\infty}=2\times 2.5=5$ +207,$dG/dF$ +208,$M = P - \mu_U= 0.505$ +209,$H_k(X)=H_k(Y)$ +210,$l(p)$ +211,$\bar Q$ +212,$L_0^{l_1} + L_{l_1}^{l_1+l_2} = L_0^{l_1+l_2}$ +213,$X''$ +214,$\mathsf{VaR}_{0.7}(X)=2.439 > 2 \times 1.204=2.408$ +215,$\mathsf{CTE}^+$ +216,$\mathbf{p}$ +217,$0 < p < 1$ +218,$\displaystyle\int_0^\infty xg'(S_X(x))dF_X(x)$ +219,$\pi=0$ +220,$h(p)=1-g(1-p)=1-(1-p)^{1/3}$ +221,$\alpha(\mathsf Q)=\infty$ +222,$\gamma$ +223,$c\ge \mathsf E[cZ]$ +224,$x\in A$ +225,"$F_n,F$" +226,$\rho(\lambda X)=\lambda\rho(X)$ +227,$\mathbf{pK}$ +228,$\mathbf{\Delta S}$ +229,$A(1_{X>x})$ +230,$g(s)=(\iota+s)/(\iota+1)$ +231,"$\max(x, 0)$" +232,$x\mapsto x^{n}$ +233,$E[G]=1$ +234,$\Lambda = \dfrac{E( r_{U} ) - r_{f}}{\sigma_{r_{U}}}$ +235,"$\{90,\dots,99\}$" +236,$g(s) \ge s$ +237,$P = 3.103$ +238,$\mathsf{MONETARY}$ +239,$p(\omega)=0$ +240,$a(X_i;X) = \lim_{t\to 0} (\rho(X+tX_i)-\rho(X))/t$ +241,"$\mathbf{X'\,\Delta g(S)}$" +242,$\sigma_{U} = \sqrt{1 - 2p - p^{2}} = 0.973$ +243,$\sigma_A$ +244,$\beta$ +245,$\mathit{NPV}_1 = \bar Q - \bar Q = 0$ +246,"$X_4, X_5$" +247,"$g:[0,1]\to[0,1]$" +248,$\mathbf{Z_2}$ +249,$X+Y$ +250,$Y=1-X$ +251,$A\subset\Omega$ +252,$g'(s)\ge 1$ +253,$K_h(t):=k(h+t)-k(t)$ +254,$\rho(X_0)\ge \mathsf E[X_0 Z_\epsilon]$ +255,$\mathscr{E}_i$ +256,$\rho_2$ +257,$\mathsf E[X\mid \mathcal F']$ +258,$y_c$ +259,$1-F(q(p));\alpha)$ +260,$w(X)=1_{X>X_p}$ +261,$\delta=0$ +262,$q(0)$ +263,$|x|$ +264,$Y_n$ +265,$X_1+({n}-X_2)$ +266,$w=0.06405$ +267,$\sum_j Y_j = 0$ +268,"$P_X(a,b]=\mathsf P(X\in (a,b])=F(b)-F(a)$" +269,$e^{kx}S(x)\to\infty$ +270,"$f(\cdot, \omega)$" +271,$N_i$ +272,$\lambda S(x)$ +273,$\rho(X)\ge \mathsf E[X]$ +274,$t=2$ +275,$\rho=\mathsf E$ +276,$\Pr(X=1)=s$ +277,$0\le s\le 1$ +278,$\mathsf{Var}^+(X) = \int_{\mathsf E[X]}^\infty (x-\mathsf E[X])^2 f(x)dx$ +279,$\rho(X) \le 0$ +280,$x_{i-1}$ +281,$Y_{0}$ +282,$\infty-\infty$ +283,$\mathsf{j}(a) = \max\{j:X_j < a \}$ +284,$s \ne s^\ast$ +285,$\mathsf E_{\mathsf{Q}}[X] = \rho(X)$ +286,$\sigma_d^2$ +287,$P=L + \iota Q = \nu L + \delta a=L(1+\rho)$ +288,$\rho(X)=x_p$ +289,"$\mu=7.4, \sigma=1.9$" +290,$\bar q(s/2)\le 2\bar q(s)$ +291,$Q_1=0.125$ +292,"$D_n, D_n^*$" +293,$a>b_h$ +294,$\sum_t Q_t$ +295,$0\le \lambda < 1$ +296,$-u''(w)/u'(w)$ +297,$q(p)=-\log(1-p)\mu$ +298,$1=v+d$ +299,$n=2$ +300,$\mathsf E[X] + \pi\mathsf E[((X-\mathsf E[X])^+)^2]^{1/2}$ +301,$X=U$ +302,$X(\omega') = \sum_\omega X(\omega)1_\omega(\omega')$ +303,$a'$ +304,$U_i$ +305,"$\bar P_{0,1}$" +306,$g_i=u_i^{1/b} < u_i$ +307,$\mathbf{D^n\rho_{X\wedge 30}(X_1)}$ +308,$\rho(X\wedge a)=\bar P(a)$ +309,$E(X\wedge a)=\bar S(a)$ +310,$1-g(0^+)$ +311,$\alpha\not\equiv 0$ +312,"$[0,1]\times [0,1]$" +313,"$X_{i,j}\Delta g(S_j)$" +314,$c_i=\displaystyle\sum_{i\not\in S\subset\Omega}\dfrac{|S|!(N-|S|-1)!}{N!}\times$ +315,"$\mathit{MV}(X, a) = a - \rho(X\wedge a)$" +316,$u'(0)=1$ +317,$S(x)=0.1$ +318,$\mathsf E X + c{X-\mathsf E X}_p$ +319,$s=0.01$ +320,$\int_a^{a+y} g(S(x))dx$ +321,$\sum X_i(a)p$ +322,$\beta(x)\le \alpha(x)$ +323,$X_1=18$ +324,$\bar P_i(a)=\mathsf E_{\mathsf{Q}}[X_i(a)]=\mathsf E[X_i(a)g'(S(X))]$ +325,$g(s)$ +326,$Z'(s)=1/(\Phi'(Z(s)))=\sqrt{2\pi}\exp(Z(s)^2/2)$ +327,$D/L$ +328,"$S\,\Delta X$" +329,$a=11$ +330,$\log(1-1/n)<-1/n$ +331,$P_i=\mathsf E_\mathsf{Q}[X_i]$ +332,"$, which he describes as the standard way to obtain the $" +333,$\phi(p) = g'(1-p)$ +334,$\mathsf{VaR}_p(X_1+X_2)\le \mathsf{VaR}_p(X_1)+\mathsf{VaR}_p(X_2)$ +335,$P(X_i(a_{gc}))$ +336,$n$ +337,$t > 1/3$ +338,"$(lee.west |- lee.north)+(0,-2.5)$" +339,$g'(S(x))f(x)$ +340,$\mathsf{Var}(\pi)$ +341,"$D^n\rho_X(X_{i,\cdot})$" +342,$-x^2$ +343,$\Pr(\{\omega \})= 1/100$ +344,$X_n\to X$ +345,$r_f/(1+ r_f) = 0.0196$ +346,$\mathbf{f}$ +347,"$\mathsf{biTVaR}_{0,1}^w(X)=(1-w)\mathsf E[X]+w\sup(X)$" +348,$D\rho_{X_n}(X_c)$ +349,$\mathsf E[F_1] > \mathsf E[F_0]$ +350,$f_{opt} =(pb - q)/b$ +351,$\{n\mid X(n)\not =0\}$ +352,$\ge 1$ +353,$n-3$ +354,$Q = C + lg$ +355,"$(1-p, 1]$" +356,$\tilde X-X$ +357,$\Delta Q_{ro}(a)$ +358,$\lim_{x\to\infty}F(x)=1$ +359,$g^{-1}$ +360,$p=0.9973$ +361,$M=P-s$ +362,$f(x_i)$ +363,$a\mathsf E_{\mathsf{Q}}[...]$ +364,$\mathcal F'_0\subset\mathcal F_0$ +365,$M/EL$ +366,$a(c_1;X) = c_1$ +367,$\mathit{EER}$ +368,"$\delta = 34/39, \nu=5/39$" +369,$\rho(X) = \mathsf E_{\mathsf{Q}}[X] = \mathsf E_{\mathsf{Q}}[X\wedge a + (X-a)^+] = \mathsf E_{\mathsf{Q}}[X\wedge a] + \mathsf E_{\mathsf{Q}}[(X-a)^+] \le \rho(X\wedge a) + \rho((X-a)^+) = \rho(X)$ +370,$A(X)-B(X)$ +371,$\rho(X\wedge a) = \sum\rho(X_i(a))$ +372,$q(0)=0$ +373,$k=c/(e^c-1)$ +374,$\Lambda = \dfrac{M - K r_f}{\sigma_U}$ +375,$\nu < 1$ +376,$\rho_g(X) = \infty$ +377,$U''(x)<0$ +378,$M = P \mu_U = 0.3$ +379,$\bar S_i(a)$ +380,$y=$ +381,$g'(S(x))=v$ +382,$\rho(X)=\mathsf E_{\mathsf{Q}}[X]=\mathsf E_{\mathsf{Q}}[\sum_i X_i]=\sum_i \mathsf E_{\mathsf{Q}}[X_i]$ +383,$\bar Q(a)$ +384,$\mathsf{j}(a)=4$ +385,$\mathsf{TVaR}_{0.8}(X)$ +386,$L/P$ +387,$\bar P(a+da)-\bar P(a)$ +388,$t+d$ +389,$\mathsf E[X]=\int_0^\infty S(x)dx$ +390,$g(0+)M$ +391,$Z(\omega)\mathsf{P}(\omega)$ +392,$t > 0$ +393,$g'(S(x))f(x)dx$ +394,$\mathsf E[h(X_i)L(X)]$ +395,$\rho$ +396,$\hat p = F(x) = 1-g^{-1}(1-p)$ +397,"$\min(x_1,x_2)$" +398,${\mathsf{Q}}$ +399,$0=\rho(0)=\rho(X-X)\le \rho(X) + \rho(-X)$ +400,$f'_-(x)\le f'_-(y)\le f'_+(y)$ +401,$\mathsf E[X_i\mid X](\omega)$ +402,$\rho(X)=\mathsf E_\mathsf{Q}[X]=\mathsf E[XZ]$ +403,"$(x_{1,1}, x_{1,2})$" +404,$\sum_n 1/n$ +405,"$\displaystyle\int_0^a \alpha_i(x)S(x)\,dx$" +406,"$\beta(X,M)=\mathsf{cov}(X,M)\sigma_M^2$" +407,$X_{-1}$ +408,$\mathcal Q=\{\mathsf Q\mid \alpha(\mathsf Q)=0 \}$ +409,$A_i$ +410,"$a(X,p)$" +411,$r\lambda\mathsf{E}[X]$ +412,"$(s,\iota)$" +413,$a-L_0^a(X)$ +414,$\mathbf{X'}$ +415,"$[p_{-},p_{+}]$" +416,$y=x$ +417,$af$ +418,$M$ +419,$\mathsf{TVaR}_{p^\ast}$ +420,$\mu=0.107$ +421,$E(X_{-1}(a))$ +422,$g'(S_X)$ +423,$j > 0$ +424,$a=\sum_i a\alpha_i(a) = \sum_i\kappa_i(a)$ +425,$\mu=0$ +426,$\mathsf E[X\wedge 0]=0$ +427,$x>1$ +428,$F(p)=p$ +429,$X_i$ +430,$q_{\tilde X}$ +431,$\omega\in \Omega$ +432,"$\var(W)=\sum_{d\ge 0} \var(Y_{-d,d})$" +433,$Y_c=(Y\mid Y > y_c)$ +434,$(m_1-m_0)/s_1$ +435,$q_B(p)=\sup B$ +436,$M_1\Delta X$ +437,"$(a,b]$" +438,$\rho(m)=\rho(0)-m$ +439,$\mathbf v$ +440,"$\omega=(1,0,0,1,0,0,\dots)$" +441,$g(S(x))=1$ +442,$0 < s < 1/4$ +443,$r_h$ +444,$X\ge a$ +445,$Q$ +446,$p\delta_p$ +447,$y^{\ast}$ +448,$\nu=1/(1+\iota)$ +449,$\mu=0.1$ +450,$s_1=0$ +451,$p=0.4$ +452,$g(S_{X}(x))$ +453,$\bar F(a):=\int_0^a F(x)dx=a-\mathsf E[X\wedge a]$ +454,$\mathsf E_{\mathsf Q}[Y]=\mathsf E[Yg'(S(X))]$ +455,$m(t^\star)=3m/4$ +456,$n_s(1-g(s))$ +457,"$g,h:[0,1]\to [0,1]$" +458,$x_{(j)}-x_{(j-1)}$ +459,$\mathsf{SRM}$ +460,$v\in V_X$ +461,$a(X_i)$ +462,$A/L$ +463,$a_{2}$ +464,$\rho_g(X)=\bar P$ +465,$\arg \min_{q \in \mathbb{Q}} E_q[U(a)]$ +466,$\Pr(X\wedge a > a)=0$ +467,$X=X_1+X_2$ +468,$\mathbf{M_{2}\Delta X}$ +469,"$n=(0.702, 1.163)$" +470,$\sum_i$ +471,$\phi'(p)$ +472,"$(X_{1,j},\dots,X_{m,j})$" +473,$E(X\wedge a)$ +474,$1/6$ +475,"$\Omega=\{\omega_1,\omega_2,\omega_3,\omega_4\}$" +476,$\nu = 1/\lambda$ +477,$\alpha \le 1$ +478,$n\times m$ +479,$\mathsf{Q}$ +480,$\mathsf E[Z]\ge 1$ +481,${6 \choose 2}=15$ +482,$\sup(\lambda X)=\lambda \sup(X)$ +483,$P+Q=a$ +484,$k=2$ +485,$f(x) \to 0$ +486,$X=1$ +487,$v_1X_1(1)$ +488,$\mathsf E[Z_1]=\mathsf E[Y]$ +489,$\pi=\Pi/p\nu(p)$ +490,$\mathcal{N}_X(X_i(a))$ +491,$\mathcal B_p$ +492,"$(p, \mathsf E[X_i\mid X=q(p)])$" +493,$S(x)\le s^*$ +494,$q_A \le q_B$ +495,"$A_2=[\epsilon, \epsilon]$" +496,$X=\sum_i X_i$ +497,$K = A - P$ +498,"$(1-g(s), 1-s)$" +499,"$r=1,2,3,4$" +500,$0=x_0a\}}$ +502,$\mathsf{Pr}(E\mid A) = \mathsf{Pr}(E\cap A) / \mathsf{Pr}(A)$ +503,$P=a - v(a-L)$ +504,$S(M-)$ +505,"$X_{t+1,2}$" +506,$7$ +507,$\nu F(a)$ +508,$\mathcal D(X)=c\mathsf{TVaR}_p(X-\mathsf E[X])$ +509,$\mu_d$ +510,"$[0,1]\to[0,\infty)$" +511,$\mathsf{SA}$ +512,$Y\le X+\Vert X-Y\Vert$ +513,$Y_1$ +514,$X=g(Z)$ +515,$\mathsf E[X_ig'(S(X))]$ +516,$\sup X=\mathsf E[XZ]=\int XZ$ +517,$Y\mid Y > y_c$ +518,$a_1' = a_0-X_1$ +519,"$X_{t-1,3}$" +520,$\mathbf{B}(t)$ +521,$\mathsf Q\in\mathcal Q(X)$ +522,$g''<0$ +523,$g(w s_1 + (1-w)s_2) \le w g(s_1) + (1-w) g(s_2)$ +524,"$k=1,\dots,m$" +525,$S_t=S_0 X_t$ +526,$\mathsf E[X\wedge a] = (1-e^{-a\beta})/\beta$ +527,$\rho(-X)$ +528,"$[s_1,1]$" +529,"$[0, 1-p]$" +530,$T = \min\{ t:U(t)\le 0 \}$ +531,$X(\omega)=1-\omega$ +532,$1-g(S(x))$ +533,$x_0=q^-(p_0)$ +534,"$\beta_i(t\mathbf{v}, x)$" +535,$\lambda=g(\lambda_{obj})$ +536,"$[-2\pi, 2\pi]$" +537,$X(\lambda\mathbf{v})$ +538,"$\bar P_{t,0} = D\rho_{W_t}(Y_{t,0})$" +539,$a>1$ +540,$a=R+Q$ +541,$k-L_0^k$ +542,$p\ge 0$ +543,$\int g(S)$ +544,$\mathsf E[X\tilde Z]$ +545,$0\le f<1$ +546,"$I(q,p)=0$" +547,$1_{X < q(1-s)}$ +548,$g - s$ +549,$x_i=1$ +550,$x\ge q(1-s^*)=:x^*$ +551,$X\succeq Z$ +552,$\Pr(X < x) \le 0.1 \le \Pr(X\le x)$ +553,$0\le w\le 1$ +554,$\mathsf{CTE}$ +555,$\iota = \dfrac{\delta}{1-\delta}$ +556,$X=x$ +557,$g^{-1}(s)$ +558,$U(0)=2$ +559,$\alpha = 0.642.$ +560,$s>1-p$ +561,$M_i := \beta_ig-\alpha_iS$ +562,${}^2$ +563,$C_c$ +564,$ROL = a + b\ \mathit{EL} + c \ C(t)$ +565,$X_2=0$ +566,$M=\delta a'$ +567,$\alpha(x) S(x)>\beta(x) g(S(x))$ +568,$P(X_{-1}(a_{gc}))$ +569,$L = \text{E}[L^*\wedge A]$ +570,$c(S)$ +571,$A\cap B\subset B$ +572,$g(s) = 1 - (1 - s)/(1 + r_f + Ck(s))$ +573,$X-b\le 0$ +574,$f(x)=(\sqrt{2\pi}x)^{-1}\exp(-(\log(x)-\mu)^2/2\sigma^2)$ +575,$r_f=0$ +576,$\mathsf{VaR}_p(X)-f(\mathsf{VaR}_p(X))$ +577,$MX$ +578,$\mathsf E_{\mathsf Q}[X_i(a)]=\mathsf E[X_i(a)g'(S(X))]$ +579,"$\displaystyle\int_0^{1-g(S(a))} \kappa_i(q(1-g^{-1}(1-p)))\,dp + a\beta_i(a)g(S(a))$" +580,$X(\omega)=\exp(10 + 2\Phi^{-1}(\omega))$ +581,$g(s)=\nu s + \delta$ +582,$W$ +583,$1_A$ +584,$f=f_x=f_{xx}$ +585,$\wedge$ +586,$g'(s)$ +587,$a$ +588,$\mathbf{Q_{1}\Delta X}$ +589,$X\wedge l$ +590,"$X_{t-d,d}$" +591,$\alpha(\mathsf Q)=0$ +592,"$\mathsf E[W]=\sum_{d\ge 0} \mathsf E[Y_{-d,d}]$" +593,$\bar q_{X_1+X_2}(s) \approx \bar q(s/2)$ +594,$X_2$ +595,"$(s,g(s))=(0.2,0.36)$" +596,$P = \mathsf E[X] + \pi\mathsf E[X]$ +597,$ \& $ +598,$\inf_x\{ x + c{(X-x)^+} \}$ +599,$P(X\wedge a)$ +600,$1-g(S(a))$ +601,"$Y_{1,0}$" +602,$s=S(x)=\Pr(X>x)$ +603,$\nu^{\ast}$ +604,$A(\lambda X)=A(\lambda X)$ +605,$dF$ +606,$\downarrow\downarrow$ +607,$\rho_2(X_1)=1$ +608,$-X$ +609,"$[x_1, x_2]$" +610,$\kappa_i(x)$ +611,$\mathsf E[(X-m)(1_{U_X\ge p}-B)]\ge 0$ +612,$r-r_L$ +613,$\alpha_i(x) S(x)$ +614,$(g(s_0)-g_0)/s_0 = g'(s_0)$ +615,"$\mathbb{Q} = \left \{ q:I(q,p) \le I^* \right \}$" +616,$\rho=0$ +617,$\mathbf{D^n\rho_{X\wedge 30}(X_2)}$ +618,$s=f'(x_0)$ +619,$\rho(X)=\sup(X)$ +620,$g(0+)>0$ +621,$\inf_x \{ x + \alpha\mathsf E[(X-x)^+] + \beta\mathsf E[(X-x)^-] \}$ +622,"$s_g, s_b$" +623,$S(x)=e^{-\beta x}$ +624,$1000$ +625,$da>0$ +626,$u'''\ge 0$ +627,$0\le \lambda_1 \le 1$ +628,$P_X$ +629,$x_1+x_2=x$ +630,$=\mathrm{MV}(X\wedge a)$ +631,$M_i(x)+Q_i(x)=\alpha_i(x)F(x)$ +632,$\delta = \iota/(1+\iota)$ +633,$a_1'=a_0-X_1$ +634,$X=\sum X_i$ +635,$X\le b$ +636,$\delta=\iota/(1+\iota)$ +637,$(\delta_p - il_p)/(\nu_p-l_p)$ +638,$x=\mathsf{VaR}_p(X)$ +639,$1200/1800=0.667$ +640,$\sigma_0=\sigma_1$ +641,$a(f + (1-f)/q) -1$ +642,$g \cdot dX$ +643,$\beta_i(a)/\alpha_i(a) < 1$ +644,$Q_{1}\Delta X$ +645,$X_g$ +646,"$X=X(x_1,\dots,x_n)=x_1X_1 + \cdots + x_nX_n$" +647,$s\leftrightarrow 1-s$ +648,$\mathcal Q_i(X)$ +649,$\mathbf{\Delta g(S)}$ +650,$V_j$ +651,$X'=X\wedge a$ +652,$20+8t$ +653,$\Delta_{2}$ +654,$\alpha_{2}$ +655,"$(1,1)$" +656,$4$ +657,"$Q_{i,j} = M_{i,j}/\iota_j$" +658,$L^\infty$ +659,$f(1)=1$ +660,"$0,10,40$" +661,$\rho(X+c)=\rho(X)+c$ +662,$H[Y_j]$ +663,$Z=(1-p)^{-1}1_A$ +664,$\mathsf E[p]=1$ +665,$\beta_i(x)g(S(x))$ +666,"$A_3=[0, \epsilon-k]$" +667,"$dx,dt,ds$" +668,$\mathsf{TVaR}_{0.95}$ +669,$f(\omega)\ge 0$ +670,$\beta=0.57$ +671,$(X\wedge a)$ +672,$X < a$ +673,$\lambda<1$ +674,"$X_{0,1}$" +675,$\omega'\not=\omega$ +676,$X_0< X_1 < \dots < X_m$ +677,$P = \mathsf E[X] + \pi \mathsf{SD}(X)$ +678,$\tilde X_1 + \tilde X_2 = X_1 + X_2$ +679,"$\{f' \in L_q \mid f'=1+f-\mathsf E f,\ \|f\|_q\le c \}$" +680,$\mathsf{VaR}\_p(X\_0)$ +681,$-(1-s)g''(1-s) + g(0+)\delta_1 + \sum_s s(g'(s-)-g'(s+))\delta_{1-s} + g'(1)\delta_0$ +682,$a>a_{ro}$ +683,$g'(0)=\infty$ +684,$(X\wedge a)/X$ +685,$\mathsf E[r] = \mu_r = M/K = 0.132$ +686,$\rho_g(V)= g(F(x^*)) \ge F(x^*)=\mathsf E[V]$ +687,$P_g\ll P_X$ +688,$Z\le (1-p)^{-1}$ +689,$F_g$ +690,$\bar P(x)$ +691,$\Pr\{a-X\le 10\}$ +692,$d^*=(\log(A/L) + (r_h-\mu_L + \sigma^2/2))/\sigma\sqrt{t}$ +693,$\mathsf E[\kappa_i(X)g'(S(X))]$ +694,"$g(s)= \displaystyle\int_0^s g'(t)\,dt = (s/(1-p)) \wedge 1$" +695,"$(s_j=0,g_j>0)$" +696,$P'<\rho(W_1\wedge a_1)$ +697,$\mathsf E[\mathsf E[X_iZ\mid X]]\not=\mathsf E[\mathsf E[X_i\mid X]\mathsf E[Z\mid X]]$ +698,$\mathsf E[S_t]=e^{\mu t}$ +699,$\mathsf{COHERENT}$ +700,$\Delta g(S_0)=1-g(S_0)$ +701,$\rho_g(V)$ +702,$X_t$ +703,$\mathsf E_{\mathsf Q}$ +704,$X_1+X_2=X=x$ +705,$v_1$ +706,$X_n\uparrow X$ +707,$\Pr(X_i>\bar q(s))=s$ +708,$m=1$ +709,$a\ge 10$ +710,$\gamma=0.633$ +711,$r=0.038$ +712,$1000(1+t)$ +713,$f(0)=0$ +714,$p(\nu(p)-l(p))$ +715,$B(X)$ +716,$h(0.9)/0.9 = 0.76$ +717,"$\int_{[0,p]} \dfrac{\mu(dt)}{1-t}$" +718,$\mathsf{TVaR}_{0.5}(X_1)=9$ +719,${}^nS(t)$ +720,$Q(a)=\nu F(a)$ +721,$\rho(X_i)$ +722,$S(x_5)$ +723,$h_x$ +724,$Y\le 0$ +725,$(I/a + U/R)$ +726,$v=1/1.1<1$ +727,$0 < r \le 1$ +728,$\{ p \mid q^-(p) \le x \}=\{ p \mid p \le F(x) \}$ +729,"$(s,g(s))$" +730,$R_f=0$ +731,$\alpha_i'(x)>0$ +732,$\lim_{s\downarrow 0} g_\tau(s) = \tau / (1+\tau)$ +733,$\mathit{NPV}_1=0$ +734,$X\wedge a\Delta S$ +735,$\mathsf{TVaR}_{0.75}(X_2)=90$ +736,$K = A-P$ +737,$A\in\mathcal F'$ +738,$\le 0$ +739,$Z'(g(s))g'(s)=Z'(s)$ +740,"$\sum_i a(X_i, p^*)=a(X)$" +741,$a_{gc}:=\mathit{VaR}_{p}(X)=18000.0$ +742,$v=1/(1+i)$ +743,"$\alpha, \beta, \kappa$" +744,$S_{X\wedge a}(x) = S_X(x)$ +745,$W_0=Y_{0} + W_1$ +746,"$s_0, s_1, s_2$" +747,$AR$ +748,$S_j:=S(X_j)$ +749,$f'_-$ +750,$\gamma=\Pr(X>\mathsf E[X])$ +751,"$ is average invested assets, equal to $" +752,$\mathsf{VaR}_{0.99}(X_2)=100$ +753,$q(F(x))$ +754,$a_i$ +755,$q=ps_g$ +756,$X_1=t$ +757,$X>Y$ +758,$M=g(S)-S$ +759,$X=1800$ +760,$g_2(s)=s^{0.5}$ +761,$xS(x)|_0^\infty$ +762,$x_h(1-p)$ +763,$v(\varnothing) =0$ +764,$\nu+\delta=1$ +765,$\rho_i$ +766,$\mathsf{SSD}$ +767,$X_i\dfrac{X\wedge a}{X}$ +768,$\varnothing$ +769,$\mathbf{X'p}$ +770,$r(X)=g'(S(X))$ +771,$X\wedge d$ +772,$1_{X>x_1}$ +773,"$\int g(S(x))\,dx$" +774,"$c(1,3)-c(3)$" +775,$\mathsf E[(X-\mu)^n]$ +776,$0.5$ +777,$A(\lambda X)=\lambda A(X)$ +778,$c=(1-\alpha)^{-1}$ +779,$\mathsf E[X_{d}]$ +780,$\mathbf{Z_1}$ +781,$M_2dX$ +782,"$(\mathsf x*0.65, 3.75*2)$" +783,$\mathit{EGL}_{ro}(a)=P(X_{-1}\wedge a) - P(X_{-1}\wedge a_{ro}) \ge 0$ +784,$2\le x\le 8$ +785,$\mathsf{CTE}_p$ +786,$\mathsf E_\mathsf{Q}\left[\dfrac{X_i}{X}(X\wedge a)\right] + \tau a \mathsf E_\mathsf{Q}[X_i/X\mid X > a]$ +787,$f(\mathsf{VaR}_p(X))$ +788,$X_n=X$ +789,"$Y_{t',d}$" +790,$D\rho_X(X_i)=D\rho_i = x_i\dfrac{\partial\rho}{\partial x_i}$ +791,$a(X)\le a(Y)$ +792,$g'(s)<1$ +793,$\mathsf E[(A-L)^+]/\mathsf E[L]$ +794,$\beta > \alpha$ +795,$\bar\iota=\iota$ +796,$\int_a^{a+y} S(x)dx$ +797,$0.125 \cdot 8 = 1$ +798,$\rho_c(X)=\mathsf E[X]+c\sigma(X)$ +799,$P = \mathsf E[Xe^{\pi X}]/\mathsf E[e^{\pi X}]$ +800,$\bar\delta(x)$ +801,$\mathsf EPD$ +802,"$\mathsf E[(X_i-\mathsf E X_i)(X-\mathsf E X)]/\mathsf{SD}(X)=\mathsf{cov}(X_i,X)/\mathsf{SD}(X)$" +803,$P_{act}-P$ +804,"$\rho(X, p^\star)=a(X)$" +805,$q(0.75)$ +806,$\mathbf{t+3}$ +807,$s=S_X(y)$ +808,$\rho l = \iota C$ +809,$\mathbf{a=1}$ +810,$\alpha(1-\alpha)(1-s)^{\alpha-1} + \alpha\delta_0$ +811,$Y_s$ +812,$\eta\nu$ +813,$(g_j-s_j)/(1-g_j)$ +814,$Z=g'(S_X(x))$ +815,$\Pr(X=x)=0$ +816,$\Delta S_5$ +817,$\mathsf E[X^k] \le \mathsf E[Y^k]$ +818,$F(x)$ +819,$D=(X-a)^+$ +820,$\sigma^2/2$ +821,$i=1$ +822,$h(p)\le p$ +823,$b = g/(1-g)$ +824,"$d=d(X_1,\dots,X_n)$" +825,$X=\max(X)$ +826,$v$ +827,$F(q(p))=p$ +828,$g(0+)=\mu(\{1\})$ +829,$X_i(a)$ +830,$p=0.999$ +831,$m\ge 1$ +832,$X_1(a)$ +833,$\Delta_s=g'(s-)-g'(s+)$ +834,$\mathsf Q \ll \mathsf P$ +835,$k/n$ +836,"$X_{t-1,2}$" +837,$d=1-v$ +838,"$f(t)=a(tx_1,\dots, tx_n)=ta(x_1,\dots, x_n)$" +839,$\partial a/ \partial v_i$ +840,$-g''$ +841,$g'(1)=0$ +842,$P(a)=g(S(a))\ge S(a)$ +843,$x\mapsto x$ +844,$x^{\ast}=\mathsf{VaR}_p(X)$ +845,"$(1,\dots,1)$" +846,$Y=-X$ +847,$\lim_{y\downarrow x} f(y)$ +848,$\iota=0.1$ +849,$A_Y = 2.155$ +850,$\Pr(S_t > a)=\Pr(X_t > a/S_0)=1-\Phi\left([\log(a/S_0)-(r-\sigma^2/2)t]/\sigma\sqrt{t} \right)=\Phi(d^*-\sigma\sqrt{t})$ +851,$g(S)=1$ +852,$X:=Y$ +853,$0.05$ +854,$\mathsf E[p] \le 1$ +855,$\Pr(E)$ +856,$xS(x)\vert_0^\infty =\lim_{x\to\infty} xS(x)=0$ +857,$k!$ +858,$602.6 billion and converted to net premium based on $ +859,$q(p)\phi(p)\times dp$ +860,$B_t$ +861,$ABC$ +862,$\lim_{x\to-\infty}F(x)=0$ +863,$\mathsf E[X^n]$ +864,$a = 0.6565$ +865,$\mu(ds)$ +866,$\mathsf E[YZ]$ +867,$p<\infty$ +868,$X_n(2/3)$ +869,$X_s$ +870,$x=q(p)$ +871,$q_X(p)=\mu+\sigma z_p$ +872,"$Y_{0,t}:=\sum_{d>t} X_{0,d}$" +873,$Z_{a}(a)$ +874,$\le p$ +875,$dx$ +876,"$G=\mathrm{cl}\{\, (\mathsf E_\mathsf{Q}[X_i], \mathsf E_\mathsf{Q}[X]) \mid \mathsf Q\in\mathcal Q \, \}$" +877,$A = 8.14864$ +878,$L(X)=1_{X=x_p}(X)/f(x_p)$ +879,$\mathbf{\mathsf E[X_i(a)]}$ +880,$\rho(X+tY)\ge \mathsf E_{\mathsf Q_X}[X+tY]$ +881,"$\{0, 8, 10\}$" +882,$P = \mathsf{TVaR}_\pi(X)$ +883,$w=w f(1)=w f(1)+(1-w)f(0) \le f(w 1 + (1-w)0)= f(w)$ +884,$Z_\mathit{lin}$ +885,$X_t=\mu t + \sigma W_t$ +886,$\alpha S$ +887,$\tilde X_1 = X_1 + \mathsf E[X_2]$ +888,$f(x)=\sin(x)$ +889,"$\Omega=\{\omega_1,\dots,\omega_n\}=\{\text{Ada}, \text{Bernhard}, \dots, \text{Zeno} \}$" +890,$\alpha(1+fg/(1-g))$ +891,$s > s_1$ +892,$t=2/3$ +893,$\int_0^s \phi(1-t)dt$ +894,$H_k(X) \le H_k(Y)$ +895,$\mathsf E[X_i/X \mid X > x]$ +896,$X\preceq Y$ +897,"$\beta_H:=\mathsf{cov}(r_H, r_M)/\var(r_M)$" +898,$1-1/c$ +899,$0 < s < 1$ +900,$\infty$ +901,$q(\hat p)$ +902,$\mathbf{\iota=M/Q}$ +903,$Z=g'(S(X))$ +904,$P=L/(1+R_L)$ +905,$n+1=N$ +906,$\rho(X_n)\not\to \rho(X)$ +907,$X'\Delta g(S)$ +908,${X}_p=\mathsf E[|X|^p]^{1/p}$ +909,$\bar M(a) = \bar P(a) - \mathsf E[X\wedge a]$ +910,$\beta_i(X_4)$ +911,$s>0.2$ +912,$\mathsf E[X1_{U_X\ge p}]\ge \mathsf E[XB]$ +913,$q_{X+c}(p)=c+q_X(p)$ +914,$X=q(F(X))$ +915,$\Pr[X > a]$ +916,$0.2 < s < 1$ +917,$t>0.5$ +918,$0 \le t \le 1$ +919,$\mathbf{Z_6}$ +920,"$\mathsf{TVaR}_p(X(x_1,x_2))=(x_1 + x_2)\mathsf{TVaR}_p(Y)$" +921,$X_1\le X_2\implies a(X_1;X)\le a(X_2;X)$ +922,$\rho_c(X)=\mathsf{TVaR}_{0.8}(X)=8.5$ +923,$\Pr(Y_m > y) = 1 - (1 - \Pr(X > y))^n$ +924,$V_X$ +925,$\mathbf{a_2'}$ +926,$\rho(1)=1$ +927,"$(3,2)$" +928,$a_2'$ +929,$\mathsf Q(A)=\mathsf E[Z1_A]$ +930,$x_{i-1}\le x'_i\le x_i$ +931,$\mathsf{TVaR}_p(X)=(12(0.9-p) + 2.5)/(1-p)$ +932,$V$ +933,"$D^f\rho_{W_t\wedge a, W_t}(Y_{0})$" +934,$\mu$ +935,$y=(\log(x)-\mu)/\sigma$ +936,$\sup(X)<\infty$ +937,$+\infty$ +938,$p=F(x)=\Pr(X\le x)$ +939,$\mathsf E[N]=2.0$ +940,$F^{-1}(p)=q(p)$ +941,$\mathbf{\max a}$ +942,$Z(y_j)$ +943,$\bar Q_{d}=a_{d}-\bar P_{d}$ +944,$\rho(X_n) \uparrow \rho(X)$ +945,$S(a)$ +946,"$\mathsf E[(X-a)^+]= p\,\mathsf E X$" +947,$(1-g(s))(1-q)$ +948,$\Delta \mathit{MV}_{gc}(a)$ +949,"$X_1,\dots,X_m$" +950,$da1_{X>x}$ +951,$g_1F$ +952,"$\bar P_{0,t}:=\rho(Y_{0,t})$" +953,$x_0+x_1+x_2$ +954,$\rho(X)=\mathsf E_{\mathbb{Q}}[X]=\mathsf E_{\mathbb{Q}}[\sum_i X_i]=\sum_i \mathsf E_{\mathbb{Q}}[X_i]$ +955,$\bar S(a)=\displaystyle\int_0^a S(x)dx$ +956,$S(X_j)>0$ +957,$f(s)=\alpha(1-\alpha)(1-s)^{\alpha-1}$ +958,"$1_A:\Omega\to \{0,1\}$" +959,$g(S(\infty))=0$ +960,"$\alpha_i(a) = \dfrac{\sum_{j:X_j>a} (X_{i,j}/X_j)p_j}{\sum_{j:X_j>a} p_j}$" +961,"$P_i,M_i, Q_i$" +962,$C'_i$ +963,$l_i$ +964,$A(c)=c$ +965,$I$ +966,$X\preceq_m Y$ +967,"$\rho(X),\rho(Y)\le 0$" +968,"$X_{0,t}$" +969,$a-X\le 0$ +970,$m_3=0$ +971,$\mathsf E[X_ie^{kX}]/\mathsf E[e^{kX}]$ +972,$\rho(W_1\wedge a_1 \wedge a_1')$ +973,"$\mathsf{CONVEX,LI}$" +974,$1_{X>x}$ +975,$\tau a$ +976,$E\in\mathcal F$ +977,$a/Q = 1 + R/Q$ +978,$\mathsf E_{\mathbb{Q}}[X_i]$ +979,$\mathsf E[X_2]=22.75$ +980,$F_Y$ +981,$X(T(U))$ +982,$\le 1/(1-p)$ +983,$\kappa_j(x)\approx \mathsf E[X_j]$ +984,$0\le \lambda\le 1$ +985,$r\times 1$ +986,$P = \mathsf E[X] + \pi \mathsf E[((X-\tau)^+)^p]^{1/p}$ +987,"$(0,1,2,3,4,5,6,7,8,9)$" +988,"$\mathsf E[X_i\,\mathsf E[Z\mid X]]$" +989,"$(3,1)$" +990,$\mathcal F_0\subset\mathcal F_1\subset \cdots\subset \mathcal F_N$ +991,$\dots$ +992,$R_C$ +993,$k = 3.3 s^{0.82}$ +994,"$X_n=1_{\{0,1,\dots,n-1\}}$" +995,$X(\omega)=x$ +996,$R_L$ +997,$D\rho_X(X_i)=\mathsf E_{\mathsf{Q}_X}[X_i]$ +998,$c(\varnothing)=0$ +999,$\mathsf E[Z\mid X]=Z$ +1000,$Q_i$ +1001,$X=10$ +1002,$P(a)$ +1003,$\rho(X)\ $ +1004,$U(1)=1$ +1005,$g(S_{X\wedge a'}(x))$ +1006,"$ occurs, i.e., those with the value 1 in the $" +1007,$\Delta X_m$ +1008,"$(0,0,0,0,0,0,0,5,0,5)$" +1009,$D=1$ +1010,$\rho(X)=\max_i \rho_i(X)$ +1011,$\mathsf E[1_{U < s}]=s$ +1012,$a_h=2-a_l$ +1013,$0 < \alpha \le 1$ +1014,"$i=1,\dots,N$" +1015,$-norm equal to 1. (Note that $ +1016,$g(0.1)=\sqrt{0.1}=0.316$ +1017,$\rho_g(X)=\mu+\lambda$ +1018,$0.5 + U/2$ +1019,$\mathsf E[Y_i\mid X_n]$ +1020,$-g'(S(x))f(x)$ +1021,$1-(p_R+p_Y)$ +1022,$\sum\mathsf E[C_i^2]=\sum m_i(1+v_i^2)$ +1023,$\Pr(X < x)\le 0.99 \le \Pr(X\le x)$ +1024,$(1+\epsilon)v_1$ +1025,$\Vert X-Y\Vert := \sup_{\omega\in\Omega} |X(\omega) - Y(\omega)|$ +1026,"$(\partial a/\partial x_1)(tx_1,tx_2)= 3tx_1 /a(tx_1, tx_2) = 3x_1 /a(x_1, x_2)=\partial a/\partial x_1$" +1027,$\beta_i(x)=\mathsf E_\mathsf{Q}\left[ \dfrac{X_i}{X}\mid X > x\right]$ +1028,$\mathsf{TVaR}_p$ +1029,$U\le u$ +1030,$-dS=f(x)dx$ +1031,$\mathbf{X_{1c}}$ +1032,$\mathsf{COM}$ +1033,$1_\omega$ +1034,$\alpha=0.5$ +1035,"$\mathsf{biTVaR}_{p_0,p_1}^w(X)=\mathsf{TVaR}_{p^\ast}(X)$" +1036,$\mathbf{x}=\mathbf{1}$ +1037,$\beta_i(x)/\alpha_i(x)$ +1038,$d^*$ +1039,$\mathsf E[q(U_X)1_{U_X\ge p}]$ +1040,$X_2-X_1$ +1041,$q_{X_i}(p)=\Phi^{-1}(p)$ +1042,$Z_a$ +1043,$\mu(\{p_0\}) = 1-w$ +1044,$Z(\omega)> 0$ +1045,$r=0.045$ +1046,$\sup_\mathsf{Q} (\mathsf E_\mathsf{Q}[X] - \alpha(Q))$ +1047,$h(s)=s^m$ +1048,$X\_{1}$ +1049,$cv=0.557$ +1050,$du = -g'(S(x))dF(x)$ +1051,$g(0)=r_0$ +1052,$M_i=\beta_ig(S)-\alpha_iS$ +1053,$j$ +1054,$g-s$ +1055,$\max_\mathsf{Q} \mathsf E_\mathsf{Q}[X]$ +1056,$w_u=1+c(1-\gamma)$ +1057,$a:=\rho(X)$ +1058,$g\Delta X \wedge a$ +1059,$\Pr(X < x)$ +1060,$M=rQ$ +1061,"$X,X_i$" +1062,$Y_c$ +1063,$($ +1064,$S_{X\wedge a}$ +1065,$\rho(1_A)$ +1066,$g_4(s)=s^{0.9}$ +1067,"$(4,1)$" +1068,$f(L)=0$ +1069,"$(-\mathsf x, 2)$" +1070,$E[(X-qp)^+]$ +1071,$I/a + U/R > 0$ +1072,$g'(S(x))=(1-p)^{-1}$ +1073,$a\le 1$ +1074,$a-b_h<0$ +1075,$\mathsf{TVaR}_p(X) := (1-p)^{-1}(T_1+T_2)/N$ +1076,$0.417 < p < 0.791$ +1077,$1-\nu p$ +1078,$\sqrt{0.9}=0.95$ +1079,"$c(1,2)-c(2)$" +1080,$\lambda X$ +1081,$r_A$ +1082,$\dfrac{\iota}{1+\iota} p$ +1083,$\rho_g(X)=452.98$ +1084,$a < \infty$ +1085,$\alpha(\mathsf Q) = 0$ +1086,$\mathsf{VaR}_p$ +1087,$Q_t=\rho(\mathsf E[X\mid t])$ +1088,$X_1=X_2=Y$ +1089,$P = 1.5$ +1090,$S(x)dx$ +1091,$L_a^{a+y}$ +1092,$\mathsf E_{\mathsf Q}[Y]=\mathsf E[YZ]$ +1093,"$\mathsf P,\mathsf Q_2,\dots,\mathsf Q_r$" +1094,$F(t)$ +1095,"$P((1+\epsilon)v_1, v_2, a+da)=P^a((1+\epsilon)v_1, v_2)$" +1096,$\mathsf E[Z(X)]=1$ +1097,$\Pr(X\le x)$ +1098,$\sum_\omega \mathsf Q(\omega) =\mathsf E[Z] / \mathsf E[Z]=1$ +1099,$\tau=0+d$ +1100,$Y=f(X)$ +1101,$a_1 = 5.991$ +1102,$\{\mathsf E_{\mathsf Q}[X_i] \mid \mathsf Q\in\mathcal Q(X)\}$ +1103,$X=X\wedge a + (X-a)^+$ +1104,"$s\wedge p=\min(s,p)$" +1105,$a=30$ +1106,$1_{U_X\ge p}$ +1107,$g(s)\ge s$ +1108,$\mathsf Q(A)>0$ +1109,$\mathsf{COH}$ +1110,$D f(x_0)$ +1111,$r_H$ +1112,$d=iv$ +1113,$U>p$ +1114,$p<0.1$ +1115,"$\mathsf{biTVaR}_{0,0.9}^{0.3138}$" +1116,$\mathsf{TVaR}_0(X)=\mathsf E[X]$ +1117,$(g(s)-s)/(1-s)$ +1118,$P/L$ +1119,$j=7$ +1120,$\mathsf E[XZ(X)]$ +1121,$\mathbf{v}'$ +1122,$0< p <1$ +1123,$\mathsf P(A)=0$ +1124,$X_{-1}=x$ +1125,$\mathbf{X'\Delta S}$ +1126,$x=q^-(p)$ +1127,$(\lambda S(x))$ +1128,$Q=1-g(S)$ +1129,$1^+$ +1130,$X \wedge a$ +1131,$\delta(s)$ +1132,"$[x, y]$" +1133,$\mathsf E X + c\mathsf E[((X-\tau)^+)^p]^{1/p}$ +1134,$\mathsf E_{\mathsf{Q}}[X] \le \rho(X)$ +1135,$\omega>0$ +1136,$K = \mathsf E[\exp (\lambda x)]^{-1}$ +1137,"$t \in (0,1)$" +1138,$1=1_{X\le a}+1_{X>a}$ +1139,$\rho(X_n)$ +1140,$Y\equiv 1$ +1141,$(dt)^{3/2}$ +1142,$m_0=0$ +1143,$\iota=\dfrac{M}{Q}$ +1144,$X\circ f$ +1145,$g(s)=s^\lambda$ +1146,$P\ge (\mathsf E[X] + \iota a)/(1 + \iota)$ +1147,"$\mathsf{MON,\ NORM}$" +1148,$\sum_i \kappa_i'(x)=1$ +1149,$ax$ +1151,$p'\ge p$ +1152,$\mathsf E[Xe^{\pi X}]/\mathsf E[e^{\pi X}]$ +1153,$\bar P_i(a)$ +1154,$Np=67.45$ +1155,$B$ +1156,"$X_n,X$" +1157,$(1-p)\gamma(dp)$ +1158,$X'=X$ +1159,$0.33$ +1160,$(1-p)/(p(\nu_p-l_p)^2)$ +1161,$\mu_U = 1-p = 0.995$ +1162,$j+1$ +1163,$q_{X+Y}=q_X+q_Y$ +1164,$\mathsf E[X_1\mid X=20]= 14$ +1165,$\mathsf Q_{X}$ +1166,"$u_{X,r}(p)=\psi_{X,r}^{-1}(p)$" +1167,$a_i=\mathsf E[X_i\mid X\ge \mathsf{VaR}_{p^**}(X)]$ +1168,$L_a^{a+da}=L_0^{a+da}-L_0^a$ +1169,$P\approx \mathsf E[A(1)] + k\mathsf{Var}(A(1))/2$ +1170,$c(X(\mathbf{v}))=c(\mathbf{v})$ +1171,$\mathsf{MRM}$ +1172,$^{*}$ +1173,"$s=0,1$" +1174,$\mathsf E[X] + \pi \mathsf{Var}(X)$ +1175,"$X(x,-x)\equiv 0$" +1176,$F(x):=\mathsf{P}(X\le x)$ +1177,$\max X$ +1178,$q=q(p)$ +1179,$1/m>0$ +1180,"$B\subset [0,1]$" +1181,$g(S(x))=1-p$ +1182,"$f:(0,1)\to (0,1)$" +1183,"$p_0,\dots, p_{n'}$" +1184,$X_1-X_0$ +1185,$\bar P = \bar S + \bar M$ +1186,$\rho(\tilde X)=\rho(X) + \rho(\tilde X-X)$ +1187,"$u\in D_n=\{ u \mid u^{(k)} \ge 0, k=1,\dots,n-1, u^{(n-1)}\text{ nondecreasing} \}$" +1188,$l(\mathbf X)=(\sum_i X_i^2)^{0.5}$ +1189,$\Pr(\cup_i E_i)=\sum_i \Pr(E_i)$ +1190,$s=S(x)$ +1191,$s_j < 1$ +1192,$\bar S(a+da)-\bar S(a)\approx \bar S'(a)da = S(a)da$ +1193,$\mathbf{\mathsf{VaR}_p(X_1+X_2)}$ +1194,$t-1$ +1195,$\mathcal D(X+c)=\mathcal D(X)$ +1196,$\tilde X_2 = X_2 -\mathsf E[X_2\mid X_1]$ +1197,$\mathsf E[X_i\mid X](x)$ +1198,"$s\in[0,1]$" +1199,$p=1-1/n$ +1200,$X(\omega)=X_1(\omega)+X_2(\omega)$ +1201,"$S(x) + d\,F(x) + (\delta^{\star}-d)\sqrt{S(x)F(x)}>1$" +1202,$S(x_#4)$ +1203,$\mathcal V$ +1204,$1-e^{-\lambda S(x)}$ +1205,$\beta>1$ +1206,$X_n=n1_A$ +1207,$d-1$ +1208,$g(S(x))\approx S(x)\approx 1$ +1209,$t_0$ +1210,$D_1$ +1211,$\mathcal E$ +1212,$\bar P=\mathsf E[W]+\lambda\sigma(W)$ +1213,$s\uparrow 1$ +1214,$Mg(0+)$ +1215,$S/L\ge A/L-1$ +1216,$\succeq$ +1217,$2\mathsf{VaR}_p(X_1) - \mathsf{VaR}_p(X)$ +1218,$Y = X + Z$ +1219,$)$ +1220,$1-(1-s)^m$ +1221,$p\to 1$ +1222,$\mathsf P(T^{-1}(A))=\mathsf P(A)$ +1223,$-zf(x)=(d/dx)g(S(x))$ +1224,$\rho_X(X_i)$ +1225,$n\Pr(Y > y_c)$ +1226,$P=\rho(X \wedge a)$ +1227,$s=0.02$ +1228,$F(q^-(p_0))=p_+>p_0$ +1229,$\Delta g(S)$ +1230,$\Delta$ +1231,"$\mu=10, \sigma=2$" +1232,$t=3$ +1233,$0\le q\le 1$ +1234,$\mathbb{Q}_k$ +1235,$L_a^y$ +1236,$X=30$ +1237,$l=\sum_i l_i$ +1238,$f:I\to\Omega$ +1239,"$f(x,y)=x^3/(x^2+y^2)$" +1240,$\Pr(X>\mathsf{VaR}_p(X))=1-p$ +1241,$g(0+)=\delta$ +1242,$S_i(x)$ +1243,$h=2$ +1244,$g'_\tau(s) = g'(s)/(1+\tau)\ge 0$ +1245,$\mathsf E_Q[X_i\mid X]=\mathsf E[X_i\mid X]$ +1246,$\mathbb{Q}(\{\omega_i\})=0$ +1247,$t \ne 0$ +1248,$\rho=\mathsf{TVaR}_p$ +1249,$\tilde M_i(a) = \bar M_i(a)-\tau_i a_i$ +1250,$a>10$ +1251,$x^+$ +1252,$A(-X)=-A(X)$ +1253,$g(s)=s^{1/3}$ +1254,$\{X = x\}$ +1255,"$p_1,p_1$" +1256,$0\le x \le 1000$ +1257,$U_s$ +1258,"$\{1,2,3\}$" +1259,$\kappa_i(x)\approx x -\sum_{j\not=i} \mathsf E[X_j]$ +1260,"$i=0,1$" +1261,$\mathsf{Var}(\Pi)$ +1262,$\mathsf E[Z \tilde X]$ +1263,$\mathsf{TVaR}_{0.75}(X_1)=10$ +1264,$g_k(s)=1-(1-s)^k$ +1265,$\mathsf E_\mathsf{P}[X_j]$ +1266,$g'(S_{X}(X))$ +1267,$(8t+10t)/2$ +1268,$\mathbf{\Sigma}$ +1269,$g(S(x_i-))=g(S(x_{i}))$ +1270,$\nu + \delta = 1$ +1271,$1-1/n$ +1272,$\Omega_1$ +1273,$\Delta g(S_j)$ +1274,$x\leftrightarrow u(x)$ +1275,$\eta=0.49$ +1276,$X=q(p)$ +1277,$\log(\mathit{EER}) = \gamma + \eta \log(\mathit{PFL}) + \beta \log(\mathit{LGD})$ +1278,$Y=-X_0$ +1279,$g'\circ S_{X\wedge a}$ +1280,$\mathsf E_{\mathsf{Q}}[X\wedge a] = \rho(X\wedge a)$ +1281,$s_2 - s_1$ +1282,$\mathbf{X_1(a)}$ +1283,$y < q_A(p)$ +1284,$\Delta\mathit{MV}$ +1285,$g'(s+)$ +1286,$w=E[w|s=0.1]=0.06405$ +1287,$f'_+$ +1288,$f_x=1/S_t$ +1289,$S(X(\omega))$ +1290,$\rho(X\wedge a)=\mathsf E[(X\wedge a)Z(X)]$ +1291,$\rho_2(X)$ +1292,$L$ +1293,$\partial a/\partial x_1=3x_1/a$ +1294,$g(s)\ge 0g(0) + sg(1)=s$ +1295,$T:\Omega\to\Omega$ +1296,$t>x$ +1297,$L^1$ +1298,$(a-X_{\mathsf{j}(a)})$ +1299,$\alpha=d_i$ +1300,"$A=\mathbb Q\cap [0,1]$" +1301,$Q_1\Delta X$ +1302,$f(L) \ge 0$ +1303,$\rho(X_1)=\rho(X_2)$ +1304,$\rho(\tilde X)$ +1305,$F_3$ +1306,$\mathsf{CTE}_p(X)$ +1307,$1_{U < s}$ +1308,$Q_2dX$ +1309,$p\to S\to gS \to \Delta gS$ +1310,$\Delta Q_{gc}(a)$ +1311,$g(s) = s^a$ +1312,$d^\ast = 1-(1-g^\ast)/(1-s^\ast)$ +1313,$g(s)=g(1-p)$ +1314,$\alpha_{Cat}$ +1315,"$\mathsf E[Y_{0,0}]+\lambda\sigma(Y_{0,0})=58.129$" +1316,"$D^f\rho_{X\wedge a,X}(X_i(a))$" +1317,$h=1+\lambda(f-\mathsf E f)$ +1318,$r_f$ +1319,$X = \sum_i X_i$ +1320,$x_3(S(x_2)-S(x_3))=x_3f(x_3)$ +1321,$\preceq_2$ +1322,$\Delta \bar Q$ +1323,$m_0$ +1324,$Q(a)=1-g(S(a))$ +1325,$\mathsf E[X\wedge a] = \dfrac{k}{\beta-1}F(a)-\dfrac{a}{\beta-1}S(a)$ +1326,$\bar P_i(x)$ +1327,$S\subset T$ +1328,$f(L)$ +1329,$D_n$ +1330,$R_M$ +1331,$Z_5$ +1332,$q^-=q^+$ +1333,$-\int xd(g\circ S)=\int g(S(x))dx$ +1334,$\tilde Z = \mathsf E[Z\mid X]$ +1335,$y\not=z$ +1336,$1-g_\tau(s)$ +1337,$\rho L = \iota Q$ +1338,$\rho(aX+bY) = a\rho(X) + b\rho(Y)$ +1339,$W \equiv T_{(1)}=min_k{T_k}$ +1340,$\lambda \rho(X)$ +1341,$Y=h(Z)$ +1342,$y^{\ast}-x^{\ast} < \epsilon$ +1343,$U/4$ +1344,$D\rho(X_0)=\{Z \}$ +1345,$X > A$ +1346,$1=\mathsf Q(\Omega)\not=\sum_n \mathsf Q(\{n\})=0$ +1347,$\sigma=0.25$ +1348,$\Delta \mathit{MV}_{gc}(a)$ +1349,$\Phi'(Z(s))Z'(s)=1$ +1350,$\bar q_{X_1+X_2}(s) \ge \bar q(s/2)$ +1351,$K = 5.029$ +1352,$1_{X>x_2}$ +1353,$S\Delta X$ +1354,$\bar{\mathbf M}$ +1355,$F_X(x):=\Pr(X\le x)$ +1356,"$G(X_1,\dots, X_n)'=(Y_1,\dots, Y_r)'$" +1357,$\mu_L=r_L +\pi$ +1358,$X=20$ +1359,$\mathsf P(X=\max(X))=0$ +1360,$r_a+r_l$ +1361,$D\rho_X(X_i) \ge \mathsf E[X_i]$ +1362,$S_1$ +1363,$\mathbf X / l(\mathbf X)$ +1364,"$w, 1-w$" +1365,$\mathcal D$ +1366,$-\rho(-X)\le \mathsf E[X] \le \rho(X)$ +1367,"$ (range.south)+(0, -1) $" +1368,$\mathsf{P}$ +1369,$X=\sum_{i=1}^n X_i$ +1370,$X_j=x$ +1371,$X_0=\mathsf E[X]$ +1372,$\Omega_a$ +1373,$\Pr(X > \mathsf{VaR}_p(X))$ +1374,$S_j$ +1375,$\beta>\alpha$ +1376,"$f(W_t,t)$" +1377,$\mathsf E[W\tilde X] \le \rho(\tilde X)$ +1378,$\mathsf E[X_ih(X)]=\mathsf E[\mathsf E[X_ih(X)\mid X]]=\mathsf E[\mathsf E[X_i\mid X]h(X)]=\mathsf E[\kappa_i(X)h(X)]$ +1379,$p\le S(x^*)$ +1380,$\phi(t)$ +1381,$S(x)=p$ +1382,$U/2$ +1383,$\int Zd\mathsf P=1$ +1384,$1+t$ +1385,$a_{1}'$ +1386,$r_h=-0.025$ +1387,"$(x_A,g(S(x_A)))$" +1388,$p(1-\nu(p))=p\delta(p)$ +1389,$\beta_i$ +1390,$1-S$ +1391,$p_{\mathit{pr}}$ +1392,$g(0+)=\lim_{t\downarrow 0} g(t)\ge 0$ +1393,$0\le \pi\le 1$ +1394,$Z=Z(X)$ +1395,$r_a$ +1396,"$\int_a^\infty g(S(x))\,dx$" +1397,$\prec X$ +1398,"$\{2, 3\}$" +1399,"$(0,1,2,3,4,8,8,8,8,9)$" +1400,$n\ge 3$ +1401,$=\mathrm{MV}(a-X)^+$ +1402,$g(s)/(1-g(s))$ +1403,$\Pr(X=y_j)$ +1404,"$E[Y\,dG/dF]$" +1405,$g(S_X(x))=1$ +1406,$q(p)=\inf\{x \mid F_X(x)\ge p \}$ +1407,$\mathit{NPV}_{\infty}$ +1408,$E[X_1 | X]$ +1409,$\beta_D$ +1410,$\sigma=0.1246$ +1411,$F(x;\alpha)$ +1412,$D_\infty$ +1413,"$(1,3)$" +1414,"$X, Y$" +1415,$q^-(p)=\mathsf{VaR}_p(X)$ +1416,"$i=1,\ldots,n$" +1417,$P/l-1 =\rho= \iota Q / l = \iota(C/l + g)$ +1418,$c(x)=\rho(\sum_i x_iX_i)$ +1419,$\omega_1=0$ +1420,$E_{\mathsf{Q_X}}$ +1421,$M_{2}\Delta X$ +1422,$S(x_#5)$ +1423,"$(\nu,\nu,\dots,\nu,\nu+10\delta)$" +1424,$\mathcal F'\subset \mathcal F$ +1425,$\Delta S_0$ +1426,$a_{d}$ +1427,$\tilde X(x) = x$ +1428,$A/L<1$ +1429,$X_n(\omega)$ +1430,$\bar P^a(\mathbf{v})$ +1431,$\int_0^1 f(s)ds = 1 - \alpha < 1$ +1432,$\mathcal{N}_{X}(X_i(a))$ +1433,$a-P$ +1434,$\mathsf{Q}(A)\le g(\mathsf{P})(A))$ +1435,$d=0$ +1436,$x\mapsto g(s)+g'(s)(x-s)$ +1437,$\mathsf{VaR}_{1-s}$ +1438,$\mathbf{Q_2\Delta X}$ +1439,$\rho_g(X\wedge a)=(\bar L + ra)/(1+r)$ +1440,$(a-X)$ +1441,$\omega'=1$ +1442,$1/6 + 2 /6 + 4/2 + 9/6$ +1443,$\rho_a(kX) = \rho(kX \wedge a(kX)) = \rho(kX \wedge ka(X)) = \rho(k(X\wedge a(X))) = k\rho(X\wedge a(X)) = k\rho_a(X)$ +1444,"$500mm, enough to materially impair their franchise, is judged to be 0.4%. This has a corresponding risk-neutral value of 2.5%. However, they believe that a loss over $" +1445,$(a_1'-a_1)^+$ +1446,$X\wedge a=\sum_i X_i(a)$ +1447,"$Q,\iota,M$" +1448,$\int_0^a g(S(x))dx$ +1449,$p>p^*$ +1450,$\{X\ge q(p)\}=\{X \ge 12\}$ +1451,$g(1)-g(0)=1$ +1452,$g(s)(1-q)$ +1453,$(g(S(x^-)-g(S(x)))/(S(x^-)-S(x))$ +1454,"$\sum_j X_{i,j}(a)\Delta g(S_j)$" +1455,"$\mathsf{P}(a,b]=b-a$" +1456,"$j=1,\dots,d$" +1457,$Z(\omega)=0$ +1458,"$\mathsf E[X_{t,d}\mid \mathcal F_0]=\mathsf E[X_{t_d}]$" +1459,$l(p)= \nu(p)-\sqrt{(1-p)/p}$ +1460,$\int_0^1 g(s)ds - 0.5$ +1461,$\rho_{g}$ +1462,$\prec_1$ +1463,$\mathsf E[X\wedge a] + d(a - \mathsf E[X\wedge a])$ +1464,$\epsilon v_1$ +1465,$\mathsf E X +\lambda {(X-\mathsf E X)^+}_1$ +1466,"$\phi(p) = (1-\alpha)^{-1}1_{[1-\alpha, 1)}(p)$" +1467,$S(M)=0$ +1468,$c\ge 0$ +1469,$\mathbf{\rho(X)}$ +1470,$p_1=1$ +1471,$\mathsf E[Z\mid X>a]=g(S(a))/S(a)$ +1472,"$x_{1,i}+x_{2,k(i)}$" +1473,"$(x_1, x_2)$" +1474,$\alpha_i'(x) \to 0$ +1475,"$\displaystyle\int_0^{F(a)} \kappa_i(q(p))\,dp + a\alpha_i(a)S(a)$" +1476,$\bar P(a)$ +1477,$q(U)$ +1478,$\iff\rho$ +1479,$F_g(x)$ +1480,$Q(a) = 1-P(a)= \nu F(a)$ +1481,$\mathsf P(\{x\})=0$ +1482,$1_V$ +1483,$R_Q$ +1484,$\mathcal D:=\{X\mid X\preceq_2 Y \}$ +1485,"$X_{j,i}$" +1486,$g(1-F(x))=1-\tilde p$ +1487,$p'$ +1488,$\beta_i(a)g(S(a))$ +1489,"$A\subset[0,\infty)$" +1490,$X_1/X$ +1491,$x$ +1492,$q_{\mathbf{v}}(p)$ +1493,$\rho(X) = \rho(X\wedge a) + \rho((X-a)^+)$ +1494,$1\not\in S$ +1495,$F(x):=\Pr(X\le x)$ +1496,$X_n=1/n$ +1497,$\rho_g(X)=\mu/b>\mu$ +1498,$\mathsf{VaR}_{0.99}(X)=1100$ +1499,$<1$ +1500,$S(X)$ +1501,$a=kP+Q$ +1502,$X\wedge a = \sum X_i(a)$ +1503,$A\subset \{ Z=0 \}$ +1504,$Z\circ T_i$ +1505,$a(X_i; X)\le \sup(X_i)$ +1506,"$Y_{1,2}$" +1507,$M_{2}$ +1508,$x \le 300$ +1509,$\implies c_i\ge 0$ +1510,$F(x)=1-s$ +1511,$h(0.9) = 1-\sqrt{0.1} = 0.684$ +1512,"$\alpha = 1, \kappa = 0.2$" +1513,$(8)(0.25)+(10)(0.25)=4.5$ +1514,$W_0=0$ +1515,$Q=S$ +1516,$X^{(d)}_i(a):=(X_i-d)^+$ +1517,${\mathcal{M}}$ +1518,$X = X_1 + X_2$ +1519,$V_t$ +1520,"$\mathsf P(\{ \omega\mid X(\omega)=X(\omega_0), \omega \le \omega_0 \})$" +1521,$\mathsf E[X_i\sum_j w_jZ_j]=\sum_iw_j\mathsf E[X_i Z_j]$ +1522,$m_3 := m_2$ +1523,$g(s)=(s+\iota)/(1+\iota)$ +1524,$\iota = \delta/\nu$ +1525,$r_X= r_f + \beta_X(r_m-r_f)$ +1526,$\mathsf E[X]+k\var(X)$ +1527,$Z\circ T\in \mathcal Q$ +1528,$\rho(X_1) \ge P_1$ +1529,$a-X$ +1530,$P(A)=1-p$ +1531,$10+0$ +1532,$\phi'(p)=-g''(1-p)>0$ +1533,"$\mathsf{TI,\ MON,\ SA,\ PH}$" +1534,$\Delta_1=a_1'-a_1$ +1535,$\mathit{RDS}_k$ +1536,$t=-ln(1-p)$ +1537,$C_i=c_i$ +1538,$\lim_{s\to 1} (g(s)-s)/(1-s) = \lim_{s\to 1} 1-g'(s)$ +1539,$\rho_i(X)$ +1540,$v(A\cap B) + v(A\cup B)\le v(A)+v(B)$ +1541,$\mathsf{TVaR}_{0.5}$ +1542,"$X_1, X_2$" +1543,$\rho=\sup$ +1544,$m_i$ +1545,$g'(s) = as^{a-1}$ +1546,$k\in\mathbb{R}$ +1547,$q(p)=F^{-1}(p)$ +1548,$E_4$ +1549,"$\psi_{X, m}(u)$" +1550,$f=(1-p)^{-1}1_A$ +1551,$<0$ +1552,$\mathbf{M}$ +1553,$X=X_1 + X_2$ +1554,$G=g$ +1555,$-q_{-Y}^-(1-p)$ +1556,"$\rho(\lambda P,\lambda R,\lambda a)=\lambda\rho(P,R,a)$" +1557,$1+bf$ +1558,$Y_j$ +1559,$\mathbf{\iota}$ +1560,$dP_g/dP_X$ +1561,$S(x)=d/dx(\mathsf E[X \wedge x])$ +1562,$M=g-S$ +1563,$FL$ +1564,$\int gS(x)dx=\int xg'(S(x))P_X(dx)$ +1565,$\mathit{MV}_{ro}(a) = a-\rho(X_{-1}\wedge a)$ +1566,$n+1$ +1567,$g'(s)=\phi(1-s)$ +1568,$X_i(a)\not= X_i\wedge a_i$ +1569,"$\mathbf{g(S)\,\Delta X}$" +1570,$\lim_{x\downarrow x_0} F(x)=F(x_0)$ +1571,$F(w) = 1-\exp(-w)$ +1572,$\mathbf{X_1/X}$ +1573,$\WCE_p(X) = \mathsf{TVaR}_p(X)$ +1574,$B_i^c$ +1575,$\Omega_a := \{\omega\in \Omega \mid (X\wedge a)=a \}$ +1576,$1/10$ +1577,$\mathsf E_{\mathbb{Q}}[(X-a)^+] \le \rho((X-a)^+)$ +1578,$Q_i(a)$ +1579,$Q>0$ +1580,$r_h-\mu_L$ +1581,$\mathbf{Z_8}$ +1582,$\mathsf E_{\mathbb{Q}}[X_i \mid X=x] = \mathsf E[X_ig'(S_X(X)) \mid X=x]/\mathsf E[g'(S_X(X)) \mid X=x] = \mathsf E[X_i \mid X=x]$ +1583,$s_j$ +1584,$\beta g(S)$ +1585,$\ge 0$ +1586,$E[u_j(W_j - X_j)]$ +1587,$\phi((x-\mu)/\sigma)/\sigma$ +1588,$X_{2}$ +1589,$E[X \wedge x+a]-E[X \wedge a]$ +1590,$\mathsf E[Z \mid X]$ +1591,$\mathsf{TVaR}_p(X)=25$ +1592,$X-(1+r)T$ +1593,"$\int_0^1 a'(tx)\,dt=\int_0^1 a(1)\,dt = a(1)=a'(x)$" +1594,$\mathsf E_{\mathsf Q}[X_i \mid X]$ +1595,$ (#1)+(#3) $ +1596,$g=F_G^{-1}(p_{\mathit{pr}})-1$ +1597,$X_{2}(a)$ +1598,$g(s)=s(1-s)$ +1599,$\mathsf{VaR}_{0.995}(U)-0.5=0.495$ +1600,$\kappa_2(10)$ +1601,$\lambda < 0$ +1602,$\mathit{ROE}(s) = fs/(1-f-s)$ +1603,$p_i$ +1604,$X_m$ +1605,$g(t) = r_0 + (1-r_0)t$ +1606,"$Y_{1,1}$" +1607,$s > s^*$ +1608,$\theta$ +1609,$g(s)=s^{1/2}$ +1610,$X\wedge a=a$ +1611,$\mathsf E[X_1Z]$ +1612,$\Pr(X\in A)=0$ +1613,$P=l + \iota Q$ +1614,$X-Y$ +1615,"$\mathbf{X\,\Delta S}$" +1616,$\log(\mathit{ROL}) = a + b \log(\mathit{EL}) + b X$ +1617,$q_{X_1+X_2}(p) \le q_{X_1}(p) + q_{X_2}(p)$ +1618,$k\ge 0$ +1619,$\Phi'(z)=\phi(z)$ +1620,$c^{-1}\log\mathsf E[e^{cX}]$ +1621,$q^-(p)=\inf \{ x \mid F(x) \ge p \}$ +1622,"$g'(s)=(1-p)^{-1}1_{[0,1-p]}$" +1623,$X(\mathbf{v})=\sum_i v_iX_i$ +1624,$s_0$ +1625,"$t=0,1$" +1626,$d^\ast = 2g^\ast-1$ +1627,"$(s_1,g(s_1))$" +1628,$g(s)=s$ +1629,$0\times\infty=0$ +1630,"$\bar Q_{0,t}:=a_{0,t}-\bar P_{0,t}$" +1631,$\mathbf{M_{1}}$ +1632,$q_X(p)$ +1633,$\rho_c$ +1634,$M(a)=g(S(a))-S(a)$ +1635,$\rho(X_n)=\rho(0)=0$ +1636,$c(S)=g(\Pr(S))$ +1637,"$\displaystyle\int_0^a \kappa_i(x) f(x)\,dx + a\alpha_i(a)S(a)$" +1638,$\mathsf E_\mathsf{Q}[X\mid A]$ +1639,$\mathbf{Z_\mathit{lin}}$ +1640,$\bar\iota = 0.12$ +1641,$\mathsf P(X=\sup(X))=0$ +1642,$\alpha_2(98)=0.9$ +1643,$p\delta(p)/p\nu(p)=\iota(p)$ +1644,$g_\tau(1)=1$ +1645,"$H(A, L, t)=LH(A/L, 1, t)$" +1646,$g_2F$ +1647,$X=X_0+X_1$ +1648,"$697.6 billion in 2016, $" +1649,$\bar Q=53.031$ +1650,$\mathsf E_{\mathsf{Q}}[\tilde X-X] \le \rho(\tilde X-X)$ +1651,$c(S\cup\{i\})=c(S\cup\{j\})$ +1652,$\mu_L=0.03$ +1653,$Q_0=\rho(V_0)=\rho(X_1)$ +1654,$g'(s-)=g'(s+)$ +1655,$\mathsf E[Xw(X)]/\mathsf E[w(X)]$ +1656,$U = X + Y$ +1657,$B=B(p)$ +1658,$\mathbf{gS}$ +1659,$9+1=10+0$ +1660,$n=67$ +1661,$a(X(\mathbf{v}))$ +1662,$v(\Omega)=1$ +1663,$p_Y=1-p_R$ +1664,"$p\,da$" +1665,$t\mapsto \rho(X+tY)$ +1666,$Y^S$ +1667,$g'(S(x)) = (1-p)^{-1}1_{x >\mathsf{VaR}_p(X)}$ +1668,$E_{\mathsf{Q_X}}[X_i(a)]$ +1669,$\rho(X)\le \rho(Y)$ +1670,$1-\tilde p=g(1-p)$ +1671,$\max_\mathsf{Q} \mathsf E_\mathsf{Q}[X] - \alpha(\mathsf Q)$ +1672,$R_f-R_L>0$ +1673,$\rho_c(X)$ +1674,$X^\star$ +1675,$X\wedge a'$ +1676,$a(W)=\mathsf E[W] + 4\sigma(W)$ +1677,$0.675=(6.258/7.613)^2$ +1678,$q<1$ +1679,$\alpha_1(90) = (0.0909 \times 0.0625 + 0.1 \times 0.0625)/(0.0625+0.0625)=0.0955$ +1680,$\mathsf E(X)=$ +1681,$g(Q)$ +1682,$\mathsf E[B]=p$ +1683,$\Pr(X< x)\le 0.75 \le \Pr(X\le x)$ +1684,"$X_2=0,0,0,0,1,1,1,4,24, 500$" +1685,$\bar P_i$ +1686,$\Pr(U\le \omega)=\omega$ +1687,$a(X)=3.769$ +1688,$\tilde X_2 = X_2 - \mathsf E[X_2]$ +1689,"$\rho(P,R,a)=\sqrt{(0.4P)^2+(0.25R)^2+(0.1a)^2}$" +1690,$\exp(x)$ +1691,$X_j$ +1692,$\mathsf E[X \mid X \ge q^+(p)]$ +1693,"$(anch.west |- lee.north)+(-0.125,0.25)$" +1694,$g(s)=20s\wedge 1$ +1695,$f(x_p)$ +1696,$\mathsf E_{\mathsf{Q}}[\cdot]$ +1697,$\Pr(X>0)$ +1698,$\{X=q_X(p) \}$ +1699,$EL(a)$ +1700,$30-11=19$ +1701,$x\in\mathbb{R}$ +1702,$p_R<0.5$ +1703,$\mathsf E[\Pi]$ +1704,$r=16$ +1705,$g(S(a))\ge S(a)$ +1706,$\beta_{1}$ +1707,$\beta_i(a)$ +1708,$N=71$ +1709,$\rho(X_1+X_2)\le \rho(X_1)+\rho(X_2)\le 0$ +1710,$a_{gc}$ +1711,"$1 between any of the layers, then $" +1712,$\mathcal{M}$ +1713,"$\sum_i \rho(X_i, p^*)=a$" +1714,$\int_0^\infty g(S(x))dx$ +1715,$t=1-p$ +1716,$\rho'(x)=U'(-x)$ +1717,"$\mathbf{D^f\rho_{X\wedge 30,X}(X_1)}$" +1718,$x=\mathsf{VaR}_{0.99}(X)$ +1719,$\alpha_i(x)-\kappa_i(x)/x=0$ +1720,$x\mapsto |x|$ +1721,$n\ge 2$ +1722,$D$ +1723,$\sigma(X)>\sigma(Y)=0$ +1724,$D\rho_X(X_2)$ +1725,$L_d^l(x)$ +1726,$\beta_1g(S)dX$ +1727,$\mathsf E[X_i]=14$ +1728,$p_j=\Delta S_j$ +1729,$x1$ +1732,$E[s|t]$ +1733,$\mathsf E[X_0]=80$ +1734,"$C(a)=\int_a^\infty S(x)\,dx + \tau a$" +1735,$\mathsf E[e^{hX}] = \exp(h\mu+\sigma^2h^2/2)$ +1736,$\beta=d^\ast-d$ +1737,$-0.00002$ +1738,$y=0$ +1739,$L_X$ +1740,$\lambda=0.5$ +1741,$g(s)=(1-p)^{-1}s\wedge 1$ +1742,$\rho(X) = \mathsf E[X] + \lambda \mathsf E[(X-\mathsf E[X])^+]$ +1743,$\sum M_i\Delta X$ +1744,$1\le x \le 2$ +1745,$f(x) \ge f(x_0) + f'(x_0)(x-x_0)$ +1746,$\mathsf E[Z_A]=1$ +1747,"$\Pr(A)\in [0,1]$" +1748,"$1,\dots,m$" +1749,$X\in L_p$ +1750,$x=1.5$ +1751,$u^{iv} \le 0$ +1752,$\mathbf{d}$ +1753,$1_{X > x}$ +1754,$S_{X_i}$ +1755,$xS(x)\to 0$ +1756,$(a-X)^+=a-(X\wedge a)$ +1757,"$j=0,1,\dots, n'$" +1758,$\mathsf{P}(\omega)$ +1759,$\beta_i(a)g(S(a))=\mathsf E_{\mathsf{Q}}[(X_i/X) \mid X>a]g(S(a))=\mathsf E_{\mathsf{Q}}[(X_i/X) 1_{X>a}]$ +1760,$\bar Q=a-\bar P$ +1761,$SdX$ +1762,$\sqrt{p}$ +1763,$L^p$ +1764,$\mu<0$ +1765,"$X_{i,i}(a)=X_{i,j}\dfrac{X_j\wedge a}{X_j}$" +1766,$\mathscr{M}$ +1767,$ so $ +1768,$1/4$ +1769,$\lambda\ge 0$ +1770,$d\bar S(a)/da=S(a)$ +1771,$(\alpha S)'(x)=-\kappa_i(x)f(x)/x$ +1772,$\sup f=1$ +1773,"$X_{t-2,3}$" +1774,$\beta_i(x)/\alpha_i(x) 0$ +1776,$\bar\nu a$ +1777,$\mathbf{\mathsf E[X_i\wedge a_i]}$ +1778,$a(1-f)$ +1779,$X\succeq Y$ +1780,$p_R$ +1781,$s_1 < s_2$ +1782,$1$ +1783,$\mathbb{Q}$ +1784,$a\le \dfrac{P-S}{\iota} + P\approx \dfrac{P-\mathsf E[X]}{\iota} + P$ +1785,$a_x=1/\lambda$ +1786,$\mathbf{\mathsf{VaR}_p(X_1)}$ +1787,$f:\mathbb{R}\to\mathbb{R}$ +1788,"$I=[0,1]$" +1789,$\rho(X)\le 0$ +1790,$B(0.5)$ +1791,$\mathsf E_G(X)$ +1792,"$i=1,2,\dots$" +1793,$r_D=1-D/L$ +1794,"$\min(X,a)$" +1795,$\Delta S$ +1796,$ is the total return on invested assets and $ +1797,$X(\psi)=X(\omega)$ +1798,$X_j\ge 0$ +1799,$\mathcal{S}$ +1800,"$i=1,\dots, n$" +1801,"$\rho_{a,\tau}(X)=v\rho(X\wedge a) + da$" +1802,"$(brR15 |- lee.south)+(-0.125,-0.25)$" +1803,$n\ge N$ +1804,$x_1 \wedge x_2$ +1805,$X_s = X_{s_1} + X_{s_2}$ +1806,$0$ +1859,$x_0 \in \{ x \mid F(x) \ge p \}$ +1860,"$\bar P(\mathbf{v}, a)$" +1861,$x_2(S(x_1)-S(x_2))=x_2f(x_2)$ +1862,$r_h=0$ +1863,"$S=[0,2\pi]$" +1864,$\mathcal E(X)=\mathsf E[(p X^+ + (1-p)X^-)/(1-p)]$ +1865,$gn$ +1866,$\mathbf{\Delta gS}$ +1867,$p=F(x)$ +1868,$\bar S_i(a) := \mathsf E[X_i(a)]$ +1869,$1/g'(s)$ +1870,$z(x)$ +1871,$-\sigma^2u''(w)\approx -cu'(w)$ +1872,$S(a+x)=d/dx(\mathsf E[X \wedge (a+x)-X \wedge a)$ +1873,$r=0.1$ +1874,$\beta_1$ +1875,"$i=1,\dots, M$" +1876,$S^{-1}(g_i)$ +1877,$X_t:=\mathsf E[X\mid \mathcal F_t]$ +1878,$\mathsf E_\mathsf{Q}[X\wedge a]$ +1879,$d =\iota/(1+\iota)$ +1880,$Z=g'(S_X(X))$ +1881,$i\not\in S$ +1882,$\mathsf E[v^T] \ge v^{\mathsf E[T]}$ +1883,$s+\delta p$ +1884,"$X_1=1+cos(X_3), X_2=1-cos(X_3)$" +1885,$(1+r)\lambda \mathsf E[X]$ +1886,$(1-p)^{-1}1_A$ +1887,$\rho=P/L-1=M/L$ +1888,$F(X)$ +1889,$\lambda=$ +1890,$\mathsf E_{\mathsf{Q}}[X]$ +1891,$\rho_g(X)=352$ +1892,$\rho(X)=\mathsf E_\mathsf{Q}[X]$ +1893,$x=0.5$ +1894,$A = -\log(p) = 5.298$ +1895,$\rho(X_{-1}\wedge a)$ +1896,$g'(S)dF(x)$ +1897,$-norm by integrating against a function with $ +1898,$(X-d)^+$ +1899,"$x=1000,2000,\ldots$" +1900,$\int_0^\infty S(x)dx$ +1901,$a=100$ +1902,$L(X)=k(X-\mathsf E X)$ +1903,"$\mathsf E[X_i] + \pi(X)\mathsf{cov}(X_i, X)/\mathsf{SD}(X)$" +1904,$+ \mathit{PV}_{r_f}(\text{Inv Inc tax})$ +1905,$S(x_1)(x_2-x_1)$ +1906,$m=q(p)$ +1907,$wx + (1-w)y\in C$ +1908,$m_X$ +1909,$A(\text{Bernoulli})$ +1910,$\mathcal{G}\subset\FF$ +1911,"$X,Y$" +1912,$\mathsf E_{QQ'}[X_i(a)] \ne \mathsf E_{QQ}[X_i(a)]$ +1913,$\tilde Q$ +1914,"$Y_{0,2}$" +1915,$E[T]=s$ +1916,$\max(X)<\infty$ +1917,$\rho(Z_2)$ +1918,$\alpha_2SdX$ +1919,$\mathsf E[\cdot\mid X]$ +1920,$c\ge 1/2$ +1921,$g(s)=\dfrac{s+\iota}{1+\iota}$ +1922,"$X_i(\mathbf{v}, a)$" +1923,$X \prec_n^* Y$ +1924,"$X\wedge a'=\min(X, a')$" +1925,$d=2$ +1926,$\mathcal D(X)=\rho(X)-\mathsf E[X]$ +1927,$s^\alpha$ +1928,$k(h):=\log\mathsf E[e^{hX}]$ +1929,$X(x)=\sum_i x_iX_i$ +1930,$\mathsf Q(\omega)=Z(\omega)\Pr(\omega)$ +1931,$1/6\le x < 2/6$ +1932,$p\ge r\ge 1$ +1933,$\rho(X_0)=\mathsf E[X_0Z]$ +1934,$\mathbf{B}(0)=\mathbf{P_0}$ +1935,$Q=(a-EL)/(1+\iota)$ +1936,$\mathsf E[Z]=\mathsf E[\mathsf E[Z\mid X]] = 0$ +1937,"$\rho(P,R,a)$" +1938,$t\mapsto v^t$ +1939,$\{ X=x\}$ +1940,$\omega \in \Omega$ +1941,"$j, p, S, \kappa_1, \Delta X, \Delta(X\wedge a)$" +1942,$0.375/1.5 = 0.25$ +1943,"$a(v_1(1+\epsilon),v_2)=a(v_1,v_2)+da$" +1944,$M_i$ +1945,$\alpha_i$ +1946,$p=1-\exp(-t)$ +1947,$\mathbf{\mu}$ +1948,$\rho(X - b)=\rho(X)-b\le 0$ +1949,$\rho(X) + c = \rho(X+c)\ge \rho(X) + \mathsf E[cZ]$ +1950,"$\boldsymbol{j, p, S, \kappa_1, \Delta X, \Delta(X\wedge a)}$" +1951,$x\ge 0$ +1952,$\rho(\lambda X) \le\lambda\rho(X)$ +1953,"$(1,1,\dots,1,1)$" +1954,$\rho(X_j)=\max_k \mathsf E_\mathsf{Q_k}[X_j]$ +1955,"$1-p, p$" +1956,$S(x)=(k/(k+x))^\beta$ +1957,$p = 0$ +1958,$\mathsf E[u(R - X)]=0$ +1959,$\var(Y_{d})=\sum_{s>d} \sigma_s^2$ +1960,$x_1$ +1961,$x=X(1-g^{-1}(1-\tilde p))$ +1962,$s < 1$ +1963,$\cdot$ +1964,$a'=a(1+r)$ +1965,$\phi(\cdot)$ +1966,"$i \in \{1,\dots,4\}$" +1967,$\gamma=r_f$ +1968,$\Delta A$ +1969,$P(X_{-1}(a))$ +1970,$0\le\lambda\le 1$ +1971,$\max$ +1972,$\Omega_0$ +1973,$\mathsf E[X^k]$ +1974,$0\le v\le 1$ +1975,$Y(\omega)=1$ +1976,$Q=A-P$ +1977,$0.75$ +1978,$a+y$ +1979,$\mathsf{Pr}$ +1980,$0.25$ +1981,$s=\mathit{EL}$ +1982,"$(1-g(S(x)),x)$" +1983,$\nu+10\delta$ +1984,$1=ps_g + (1-p)s_b$ +1985,$U(1)=2$ +1986,$\bar S_i(a)=\mathsf E[X_i(a)]$ +1987,$\Phi(-d^*)>0$ +1988,$\Pr(X\ge q(p))>1-p$ +1989,$x\to\infty$ +1990,$g(pq)=g(p)g(q)$ +1991,$P = \mathsf E[X] + \pi \mathsf E[|X-\mathsf E[X]|^p]^{1/p}$ +1992,$\frac{d}{dp}(1-p)^{-1}=(1-p)^{-2}=q^{-2}$ +1993,$\mathsf E X + c{(X-\tau)^+}_p$ +1994,$\rho(X)<\infty$ +1995,$\mu_L=r_L + \pi$ +1996,"$k=(0.04, 0.4)$" +1997,$\Delta S=p$ +1998,"$A,B$" +1999,$N(1-p)$ +2000,"$(\omega'=1, \omega'')\in B_k$" +2001,$P = \mathsf E[X] + \pi \mathsf E[((X-\mathsf E[X])^+)^p]^{1/p}$ +2002,$\mathbf{t}$ +2003,"$p_0,\dots, p_m$" +2004,$\tilde Z$ +2005,$\tilde X+X$ +2006,$dF(x) = dp$ +2007,$x_0 < \mathsf{TVaR}_{p_0}$ +2008,$\lambda\sigma$ +2009,$\mathsf E[(X-m)(1_{U_X\ge p}-B)] = 0$ +2010,$Z_j$ +2011,$m'(1) \to -1$ +2012,$\mathsf E[X\mid \mathcal F_{t+1}]$ +2013,$g(S_j)$ +2014,$g(s(t)) = m(t)+s(t)$ +2015,$A\subseteq \mathbb{R}^N$ +2016,$f(x)\ge f(x_0) + s(x-x_0)$ +2017,$p=0.9982$ +2018,$a=10$ +2019,$\mu + \lambda\sigma$ +2020,$\beta<\alpha$ +2021,$Z\ge 0$ +2022,$\bar\nu(x)$ +2023,$\mathsf E_\mathsf{Q}[X]\le \mathsf E_\mathsf{Q}[Y]$ +2024,$\mathbf{Z_3}$ +2025,$6.258$ +2026,$\rho(X)=-\rho(-X)$ +2027,$-\sigma^2/2$ +2028,$k>0$ +2029,$r = 0.12$ +2030,"$(3,4)$" +2031,$dG/dF=r(x)$ +2032,$F_0=2.5$ +2033,$F_g(b)-F_g(a)=g(S(a)) - g(S(b))$ +2034,$P_g$ +2035,$\kappa_i(x)=\mathsf E[X_i\mid X=x]$ +2036,$\bar S$ +2037,$p=F(a)=1-s$ +2038,$Z(\omega)<1$ +2039,$\alpha\equiv 0$ +2040,$Var(G)=c^2$ +2041,$a = a(X)$ +2042,"$x\in\Omega=[0,1]^N$" +2043,$1_{U_X\ge p}=1$ +2044,$r_h<0$ +2045,$g(S(x_i)-g(S(x_i-))$ +2046,$F(a)$ +2047,$L_d^{d+l}(x)=(x-d)^+ \wedge l$ +2048,$X_3$ +2049,$\bar P(a+y) - \bar P(a)$ +2050,$\bar P$ +2051,$x_{i+1}$ +2052,$-X_2$ +2053,$M_2\Delta X$ +2054,$(1+r)\mu$ +2055,$\bar P^a$ +2056,$\ge p$ +2057,$\mathsf E X + c\mathsf E[\vert X-\tau \vert^p]^{1/p}$ +2058,$\\mathbf{\1}$ +2059,$\displaystyle\int_0^\infty u(x) g'(S_X(x)) dF_X(x)$ +2060,"$\omega\in [k2^{-m}, (k+1)2^{-m}]$" +2061,$p=2$ +2062,$X=98$ +2063,"$0\le U, V\le 1$" +2064,$Y'$ +2065,$\displaystyle\int_0^\infty xf(x)dx$ +2066,$(1-g(s))/(1-s)$ +2067,$\mathsf E[X_i]/x$ +2068,$00$ +2079,$X_{1}(a)$ +2080,$\psi(u)=\Pr(Y > u)$ +2081,$\mathsf E[\cdot]$ +2082,$\Delta(X\wedge a)$ +2083,$P = S + M$ +2084,$(0.304-0.2)/(1-0.304) = 15$ +2085,$\mathsf E_{\mathbb{Q}}[X\wedge a] \le \rho(X\wedge a)$ +2086,$\omega_2$ +2087,$P/S-1$ +2088,$g(s)/s$ +2089,$\mathbf{S\Delta X}$ +2090,"$h(x)=\sup_{s\in[0,1]} g(s)-sx$" +2091,$C(t)$ +2092,$t=4$ +2093,$i^*$ +2094,$\rho(X)=\mathsf E[X] + c\sigma(X)$ +2095,$g(1)=1$ +2096,$C'_1+\cdots + C'_n$ +2097,$\mathsf E[X]=\sum_{\omega\in\Omega} X(\omega)\Pr(\omega)$ +2098,$E_i\cap E_j = \varnothing$ +2099,$s_1$ +2100,$BY \succ AR$ +2101,$0.8 \times 1.2 = 24/25$ +2102,$(g(s)-s)/(1-g(s))$ +2103,$a = 8.1484$ +2104,$Y\circ T_i$ +2105,$p=0.9999$ +2106,$Z_X$ +2107,$\beta_i(x) =\mathsf E_{\mathsf Q}[X_i/X\mid X>x]$ +2108,"$X_{0,1},X_{0,2},\dots, X_{0,N}$" +2109,$Z=0$ +2110,$\rho_g(X)=\mathsf E_{\mathbb{Q}}[X]$ +2111,$-k$ +2112,$\mathsf E_\mathsf{Q}[X]=\mathsf E[XZ]$ +2113,$v(A)=g(\mathsf{P}(A))$ +2114,"$\bar P_i(\mathbf{v}, a)$" +2115,$B_p$ +2116,$a_i=x_i(\partial a/\partial x_i)$ +2117,$N$ +2118,$\sup$ +2119,$\rho(\tilde X)=\mathsf E_{\mathsf{Q}}[\tilde X]$ +2120,$q_X(p)\le q_Y(p)$ +2121,$S(x)=s$ +2122,$X\preceq_n Y$ +2123,"$y,z\in X$" +2124,$\Omega_0 \times \Omega_1$ +2125,$df/dx=f$ +2126,$\mathsf{TVaR}_p(X)$ +2127,$X=8$ +2128,$Q\in\mathcal{Q}$ +2129,$0.125$ +2130,$P(X_{-1}\wedge a)$ +2131,$s < p$ +2132,"$n=1,2,\dots, m-1$" +2133,$S(x)\approx 1$ +2134,"$X_2=(0,1,2,3,4,8,6,4,0,9)$" +2135,$1.5$ +2136,$q_X(p) = X(T(p))$ +2137,$1-m\le 1$ +2138,$\mathsf E_\mathsf{Q}[X_1]$ +2139,"$k=1,\dots, n-1$" +2140,$X_{-1}+X_{0}$ +2141,$p<0.05$ +2142,$\delta$ +2143,"$\gamma([0,p])=C(p)$" +2144,$10$ +2145,$T(U)$ +2146,$\rho_a(X+c) = \rho((X+c)\wedge a(X+c)) = \rho((X+c)\wedge (a(X)+c)) = \rho((X\wedge a(X))+c) = \rho((X\wedge a(X))) + c=\rho_a(X)+c$ +2147,$\bar M_t$ +2148,"$x~\text{Unif}[0,1]$" +2149,$g'(S(X))$ +2150,$\tilde Z=\mathsf P(X=\sup(X))^{-1}1_{X=\sup(X)}$ +2151,$\bar P(a+da) -\bar P(a)$ +2152,$X(x)=1/x$ +2153,$x=\mathsf{VaR}$ +2154,$\beta_2g(S)dX$ +2155,$\sigma(X_d)$ +2156,$\mathsf Q(X>a)/\mathsf P(X>a)$ +2157,$\mu(dp)$ +2158,$c=(g-s)/(g(1-g))$ +2159,$\mathsf E[Y_d]$ +2160,$X\wedge a=a=90$ +2161,$\sigma(W)$ +2162,$1\le p\le \infty$ +2163,$X=4$ +2164,"$\sigma(L^\infty, L^1)$" +2165,$p_0\not= p_1$ +2166,$\mathsf E[X]+k\mathsf{Var}(X)=a(X)$ +2167,"$a_{0,0}'=a_{0,0}$" +2168,$\{\omega\mid X(\omega) > x\}$ +2169,$P_i$ +2170,$\lambda_2\not=1$ +2171,$p>0.9$ +2172,$E(X^k)=E(Y^k)$ +2173,$=v_f \mathsf E_\mathsf{Q}\left[\dfrac{X_i}{X}(X\wedge a)\right]$ +2174,$\bar P_t$ +2175,"$\Omega=\{ 1,2,3,4,5,6 \}$" +2176,$p<0.7$ +2177,"$a=10,20,40,50,60$" +2178,$-\infty+\lambda=-\infty$ +2179,$x=y$ +2180,$d=0.1/1.1$ +2181,$\beta_2>\alpha_2$ +2182,$\rho(X)=\mathsf E_{\mathsf Q}[X]$ +2183,$\Pr(E')+\Pr(E)=\Pr(\Omega)=1$ +2184,$v_f(\mathsf E_Q[X_i] - \mathsf E_Q[X_i/X(X-A)^+])$ +2185,$=\displaystyle\int_0^\infty x dF(x)$ +2186,$\mathcal Q=\{\mathsf Q_k\}$ +2187,$a(f + (1-f)/q)$ +2188,$\mathsf E_\mathsf{Q}[\cdot]$ +2189,$\lfloor x \rfloor$ +2190,$A\in\mathcal F$ +2191,$\mathsf E X + c\mathsf E[((X-\mathsf E X)^+)^p]^{1/p}$ +2192,$v(A)=\lambda(\pi_1(A))$ +2193,$\mathbf{M_{2}}$ +2194,$n\to\infty$ +2195,$\beta_i(x) =\mathsf E_{\mathsf{Q}}[X_i/X\mid X>x]=\mathsf E[(X_i/X)g'S(X))\mid X>x]$ +2196,$\Longleftarrow$ +2197,"$\eta_{p,\alpha}$" +2198,$\Omega$ +2199,$\mathsf{QCX}$ +2200,$\omega=\omega'$ +2201,$g(S_{\mathsf{j}(a)})(a-X_{\mathsf{j}(a)})=(0.5)(80-11)=34.5$ +2202,$z_p=\Phi^{-1}(p)$ +2203,$g_1(s)=s^{0.4}$ +2204,"$1-e^{-\lambda S(\mathsf{PML}_{n, \lambda})}=1/n$" +2205,$\mathbf{X_2/X}$ +2206,$\mathbf{\alpha_1S\Delta X}$ +2207,$q^-(U)$ +2208,$\mathbf{g_3(s)=s^{0.7}}$ +2209,$s=\exp(-a/b)$ +2210,$F(x)\ge p\iff q^-(p)\le x$ +2211,$\mathsf E_\mathsf{Q}[X]$ +2212,$(P-L)/L=P/L-1$ +2213,"$[p,1]$" +2214,$F_2$ +2215,"$\{H,T\}$" +2216,$\mathbf{g(S)}$ +2217,$a(1-p) + \mu p - \sigma\phi(z_p)$ +2218,"$(p, \mathsf E[X_i\mid X=q(1-g^{-1}(1-p))])$" +2219,$\rho(b-X)=b+\rho(-X)$ +2220,$s<1$ +2221,$g''(s)=-s^{3/2}/4$ +2222,$D^n\rho_X(X_1)=6.2048$ +2223,$\Delta X\wedge a$ +2224,$v=1/(1+r)$ +2225,$v_f\mathsf E_Q[X_i]$ +2226,$(1-p)^{-1/2}/4$ +2227,$T(X):=y\wedge (X-r)^+$ +2228,$x=S^{-1}(g^{-1}(u))$ +2229,$A(X+c)=A(X)+c$ +2230,$\mathit{EGL}_{gc}(a)$ +2231,"$c\in[0,1/2]$" +2232,$\sigma=2.58$ +2233,$a_x=4$ +2234,$dp=\exp(-t)dt$ +2235,"$\beta_i(a) = \dfrac{\sum_{j:X_j>a} (X_{i,j}/X_j) \Delta g(S_j)}{\sum_{j:X_j>a} \Delta g(S_j)}$" +2236,$X = X\wedge a + (X - a)^+$ +2237,$(1-p)/(p\nu_p^2)$ +2238,$u$ +2239,$\omega$ +2240,$\mathsf{TVaR}_{0.8}(X+tX_1)$ +2241,$\Pr(X > x)$ +2242,"$\rho_g(X)= \sum_j X_j\,\Delta g(S_j)$" +2243,"$X_1,\dots,X_n$" +2244,$D\rho_{X}(Y) \subset D\rho_{X\wedge a}(Y)$ +2245,$\lambda=\dfrac{1}{1+\rho}$ +2246,$q^-(s)=\mathsf{VaR}_s(X)$ +2247,$=v_f \mathsf E_Q\left[\dfrac{X_i}{X}(X\wedge A)\right]$ +2248,$v_i$ +2249,"$p=0.01, 0.02, \dots, 0.99$" +2250,$\mathsf{VaR}\_p(X)$ +2251,$a_0$ +2252,$0\le b\le 1$ +2253,"$A=(a,b]$" +2254,$\rho(X)=\max_\mathsf{Q} \mathsf E_\mathsf{Q}[X]$ +2255,$a(\mathbf{v}) =\mathsf{TVaR}_p(X(\mathbf{v}))= (1-p)^{-1}\int_p^1 q_{\mathbf{v}}(s)ds$ +2256,$-g$ +2257,$q^-(p) := \sup\ \{x \mid F(x) < p \} = \inf\ \{ x \mid F(x) \ge p \}$ +2258,$p(\omega)\ge 0$ +2259,$D/L>1$ +2260,$\rho(X)=\mathsf E[f_X X]$ +2261,$-m_2/(1-s_2)$ +2262,$g(1-F(x))=1-p$ +2263,$h(1_{X\le a})$ +2264,$E(\pi)$ +2265,$\mathsf{TVaR}_{0.95}(X)$ +2266,$b-X\ge 0$ +2267,$Z = \sum_j X_j$ +2268,$X+Z$ +2269,$\mathsf{VaR}_{0.75}(X)=90$ +2270,$QR_Q = aR_A + PR_L$ +2271,$x=\lambda y + (1-\lambda)z$ +2272,$dS=-dF$ +2273,$\mathsf E[X_i \mid X=q(p)]$ +2274,$s \to 1$ +2275,$\mathsf E[X]\le \mathsf E[Y]$ +2276,$\tilde M(a)=\bar M(a)-\tau a$ +2277,$P = \log(\mathsf E[e^{\pi X}])/\pi$ +2278,"$(-\mathsf x*.8, 2*2)$" +2279,"$(ccc.south |- mcc.south)+(0,-0.5)$" +2280,"$[0,1]\to[0,1]$" +2281,$p=\infty$ +2282,$\bar P(a) = \rho_g(X\wedge a)$ +2283,$0\rho_2(X)$ +2285,$s(t)$ +2286,$\rho(W_1\wedge a_0)$ +2287,$0.8 \le p < 0.9$ +2288,$\epsilon_2$ +2289,$k=0$ +2290,$\Delta X_j=X_{j+1} - X_j$ +2291,$\iota:1$ +2292,"$x_{2,1}$" +2293,$Y_{d}=\sum_{s>d} X_{s}$ +2294,"$\phi(x_1,...,x_n)$" +2295,$Z\in\mathcal Q$ +2296,$\mathbf{Z_7}$ +2297,$\iota^\ast$ +2298,$X-P$ +2299,$g(s)q=0.1839$ +2300,$X_2=x-t$ +2301,"$X_{t+2,1}$" +2302,$\mathsf{MON}$ +2303,$G(x)= 1-g(1-F(x))$ +2304,$g'(s)\to\infty$ +2305,"$j \in \{5,\dots,8\}$" +2306,$e^{-r_Dt}$ +2307,"$\mathbb{R}=(-\infty, \infty)$" +2308,$\rho((X-a)^+)$ +2309,$Q_t$ +2310,$\Pr(B)=0$ +2311,$X_0 < \dots < X_{N-1}$ +2312,$\Pr(X=x_i)=\lambda_i/\lambda$ +2313,"$B_4 = [\epsilon_1, \epsilon_2]$" +2314,$a(w_1X_1+w_2X_2;X)=w_1a(X_1;X)+w_2a(X_2;X)$ +2315,$(P-L) / (A-P)=$ +2316,$AR\succ BR$ +2317,$\mathsf E[X\wedge a]= 2.4982$ +2318,$a(x)=xa(1)$ +2319,$X(\mathbf{v})$ +2320,"$x_{1,1}$" +2321,"$d, r>0$" +2322,"$\phi(s)= g'(1-s) = \frac{1-w}{1-p_0}1_{[p_0, 1)}(s) + \frac{w}{1-p_1}1_{[p_1, 1)}(s)$" +2323,"$S\subset \Omega=\{1,\dots,N\}$" +2324,$\rho(\mathsf E[X_2\mid X_1])\le \rho(X_2)$ +2325,$x\le 0$ +2326,$\mathbf{d=1}$ +2327,$S_0=1$ +2328,$f(x)=|x|$ +2329,$S_t \ge 0$ +2330,$p=F(a)$ +2331,$\Psi^{-1}(t)=\log(-\log(t))$ +2332,$\mathsf E[X\mid X>2000]-2000=\mathsf{TVaR}_{F(2000)}(X)-2000=624$ +2333,$q(U_X) > m$ +2334,$Y_s=(Y\mid Y\le y_c)$ +2335,$\mathsf{P}(d\omega)$ +2336,$h(0)$ +2337,$\mathbf{Z_\mathit{lift}}$ +2338,$P_i/v_i$ +2339,$\lambda > 0$ +2340,"$c(1,2) - c(2)$" +2341,"$(0,1]$" +2342,$t<0$ +2343,$\mathsf{COMON}$ +2344,$\beta_i(x)/\alpha_i(x)> 1 > g(S(x)) / S(x)$ +2345,$\mathsf E[XM]$ +2346,$\int_0^\infty (1-F(x))dx=\int_0^\infty xdF(x)$ +2347,$(dW_t)^2=dt$ +2348,$\mathbf{a=0.93}$ +2349,$\mathsf{TVaR}_{0.95}(X)=3699$ +2350,$g(0^+) = r/(1+r)$ +2351,$x\mapsto 1/x$ +2352,$m\in\mathbb{R}$ +2353,$-S(a)+\tau=0$ +2354,$\mathsf{VaR}_{0.7}(X_i)=-\log(0.3)=1.204$ +2355,$\rho(c)\ge c$ +2356,$\beta_i(X)$ +2357,$0.8\le p<0.9$ +2358,$\mathsf P(X \le q_X(p)) > p$ +2359,$1/X$ +2360,$\displaystyle\int_0^1 X(p)dp$ +2361,$\kappa_1(x)=\mathsf E[N_1/(N_1+N_2)]x$ +2362,$\rho_c\leftrightarrow\mathcal Q$ +2363,$U(X)\ge U(Y)$ +2364,$ = \mathsf E_{\mathsf{Q}}[X_i\mid X= x]$ +2365,$\lambda X_1 +(1-\lambda) X_2$ +2366,$MV = \bar Q + \mathit{NPV}_{\infty}$ +2367,$g(s)=1-(1-s)^m$ +2368,$g(0.05)=0.05\nu + \delta=0.1364$ +2369,"$\mathcal F_0=\{\varnothing, \Omega\}$" +2370,$p(x) = \Pr(\{\omega\mid X(\omega) = x\})=\Pr(X=x)$ +2371,$g(S(x)) = 1 - h(F(x))$ +2372,$g(s)\le s$ +2373,$L_1$ +2374,$X_1=1000$ +2375,$S$ +2376,$x < y$ +2377,$p>0.5$ +2378,$x=(y-\mu)/\sigma$ +2379,$a\to\infty$ +2380,$X+tX_1$ +2381,$M = \beta g(S)-\alpha S$ +2382,$0 < \nu = 1-\delta < 1$ +2383,$d=(\log(a/S_0)-(r-\sigma^2/2)t)/\sigma\sqrt{t}$ +2384,$X(\omega)=1/\omega$ +2385,$1/n$ +2386,$\mathsf E[X] + \pi\mathsf E[X]$ +2387,$H(X)>-H(-Y)$ +2388,$s/(1-p) \wedge 1$ +2389,$\mathsf E[X] + \pi\var(X)$ +2390,$\Phi$ +2391,$\lambda y=x$ +2392,$\mathsf{MON'}$ +2393,$g'(S_X(X))$ +2394,$b<1$ +2395,$w < s$ +2396,$m_2$ +2397,$\le c$ +2398,$n-1$ +2399,$qX$ +2400,$\bar P_2$ +2401,"$(4,3)$" +2402,$(X_i)_i$ +2403,$20+10t$ +2404,$s=1-\alpha$ +2405,$Z=d\mathsf Q / d\mathsf P\ge 0$ +2406,$X_i(a) = aX_i/X$ +2407,"$c(1,2,3)-c(2,3)$" +2408,$\sum_i q_iX_i$ +2409,$\mathbf{Q_{2}\Delta X}$ +2410,"$H_k(X):=\mathsf E[\max(X_1\dots, X_k)]$" +2411,$\kappa_j(x)/x > \alpha_j(x)$ +2412,$a_i'$ +2413,$-\int xdS=\int Sdx$ +2414,$c\ge 1$ +2415,$\mathbf{B}(1)=\mathbf{P_3}$ +2416,"$\bar Q_{0,0}:=a_{0,0}-\bar P_{0,0}$" +2417,$p_- < p_0 < p_+$ +2418,$g'(t)=1-r_0$ +2419,$q(p)=\mathsf{VaR}_p(X)$ +2420,$g(0+):=\lim_{s\downarrow 0}g(s)$ +2421,$z\ge 0$ +2422,$ \& $ +2423,$A\setminus B$ +2424,$(k_1!)(k_2!)\dots$ +2425,$Q(x)=1-P(x)$ +2426,$\sup(X)$ +2427,$1=\delta+\nu$ +2428,$=1/\lambda-1=(1-\lambda)/\lambda$ +2429,$U_X$ +2430,"$\mathbf{X\,\Delta g(S)}$" +2431,$\mathit{EGL}_{ro}(a)$ +2432,$q_X$ +2433,"$i=1,2,\dots,10000$" +2434,$Z=z(X)$ +2435,$\bar{\mathbf P}$ +2436,$\{X > x \}$ +2437,$X_{\mathsf j(a)+1}>a$ +2438,$g_j<1$ +2439,$\rho(X)=0$ +2440,$\sum_i x_iX_i$ +2441,$Xq$ +2442,$\phi(p)=g'(1-p)=b(1-p)^{b-1}$ +2443,$N=1000$ +2444,$\mathsf E_{\mathsf{Q}}[X]=\infty$ +2445,$A\subseteq \mathbb{R}^n$ +2446,$a=90$ +2447,"$g:[0,1]\to [0,1]$" +2448,$q(p)$ +2449,$g(s)=\nu s+\delta$ +2450,$m=$ +2451,$\mathbb{Q}\in\mathcal Q$ +2452,"$q(p)\phi(p)\,dp$" +2453,$x>\mathsf{VaR}_p(X)$ +2454,$\hat x > x$ +2455,$\text{VaR}_{0.99}$ +2456,$P_X\{X=M\}=0$ +2457,$X=X_0+X_{-1}+X_{-2}+X_{-3}$ +2458,$x>0$ +2459,"$X_{i,j}$" +2460,$a_1=\int_0^1 (\partial a/\partial x_1)dt=\partial a/\partial x_1$ +2461,$\mathsf E[X(1_{U_X\ge p}-B)]=\mathsf E[(X-m)(1_{U_X\ge p}-B)]$ +2462,$1=\bar\nu+\bar\delta$ +2463,$(1-p)/p=1$ +2464,$\mathsf E[X_i(v_i)]=v_i\mathsf E[X(1)]$ +2465,$s=S(a)$ +2466,$\partial\rho(Z)$ +2467,$\mathbf X$ +2468,$\rho(W_1\wedge a_1 \wedge (a_0-X_1))=\rho(W_1\wedge a_1)$ +2469,$\sum_i \kappa_i(x)=x$ +2470,$(g(s_0)-g_0)/s_0 \ge g'(s_0)$ +2471,$g(s)=s^{0.4}$ +2472,$X_n(0)=1$ +2473,"$X_{t,2}$" +2474,$W=Z$ +2475,$\phi(x):=(2\pi)^{-1/2}\exp(-x^2/2)$ +2476,$g(s)=\sqrt{s}$ +2477,$1-p=S(x)$ +2478,$\mathsf E_{\mathsf{Q}}[Y \mid X] = \mathsf E[Y \mid X]$ +2479,$p(\delta_p-il_p)$ +2480,$\alpha(X)$ +2481,$=1$ +2482,$g''$ +2483,$f=f_X$ +2484,$dW_t\approx W_{t+dt}-W_t$ +2485,$X(\omega_1) > Y(\omega_1)$ +2486,$H_g(X) \le H_g(Y)$ +2487,$M:=\max(X)$ +2488,"$0,10,20$" +2489,$1/9=0.11\dot 1$ +2490,$a=80$ +2491,$n-2$ +2492,"$((0, x), (1-p, p))$" +2493,$P=D=L/(1+R_L)$ +2494,$w(A)\le v(A)$ +2495,$\Pr(X\ge x)\ge 1-p\ge \Pr(X> x)$ +2496,$2^{20}\approx 1$ +2497,$^{**}$ +2498,$\mathbf{X_{g}}$ +2499,$\mathsf{LI}\iff\mathsf{SSD}$ +2500,$p_j$ +2501,$P$ +2502,$s_0\mathsf{VaR}_p(X)]$ +2530,$\mathcal M_\rho=\{ m \}$ +2531,$\mathsf E[kX]$ +2532,$f(p)=\alpha(1-\alpha)(1-p)^{\alpha-1}$ +2533,"$L_a^{a+y}(x)=\min(y, \max(x-a,0))$" +2534,$(X-a)^+$ +2535,$\omega''$ +2536,$0.20$ +2537,$g(X_n)=1$ +2538,$M_i\Delta X$ +2539,$p=0.01$ +2540,$w=0$ +2541,$f'_-(x)=\lim_{h\uparrow 0} (f(x+h)-f(x))/h$ +2542,$B_1 \succ A_1$ +2543,$1-f$ +2544,$X_0 < X_1 < \dots < X_{n'}$ +2545,$a=$ +2546,$Q_{2}\Delta X$ +2547,$\kappa_i'(x)=1$ +2548,$X'\Delta S$ +2549,$a=\alpha(X)$ +2550,$X_2=1000$ +2551,$\alpha(\mathsf P)=0$ +2552,"$h(p)=p/(1+\iota(p))=\nu(p)\, p$" +2553,$\mathsf E[X_2\mid X=20]=6$ +2554,"$s,p$" +2555,$F(x)=u$ +2556,$a_i = \mathsf{VaR}_p(X) - \mathsf{VaR}_p(\sum_{j\not=i} X_j))$ +2557,$z(X)$ +2558,$n_s\ge 0$ +2559,$x_6^1+x_6^2=10+1=11=x_6$ +2560,$g(S(x)$ +2561,$0\le \lambda \le 1$ +2562,$(\mu-\sigma^2/2)t$ +2563,$(\delta^{\star}-d)\sqrt{S(x)F(x)}$ +2564,"$\alpha_p = 1- (\| (X-\eta_{p,\alpha})^+\|_{p-1} / \| (X-\eta_{p,\alpha})_- \|_{p})^{p-1}$" +2565,$\alpha (1-s)^\alpha/(1-s)$ +2566,$d\to\infty$ +2567,$p(\nu_p-l_p)$ +2568,$g(s)=s^2$ +2569,$a=a(\mathbf{v})$ +2570,$\sup_\mathsf{Q} \mathsf E_\mathsf{Q}[X]$ +2571,$\int_0^1 1-g(s)ds=1-\int_0^1 g(s)ds < 0.5$ +2572,$X_i>0$ +2573,$i= \alpha/(1-\alpha)$ +2574,$X\ge x$ +2575,$Z(x)=g'(S(x))$ +2576,"$c = 1.0, 1.5$" +2577,$a_{d}=a(Y_{d})$ +2578,$\mathsf{SD}(X)$ +2579,$-A(-X)$ +2580,$t\ge 0$ +2581,"$\Omega=\{0,\dots,99\}$" +2582,$g'(S(x))\ge 0$ +2583,"$p~\text{Unif}[0,1]$" +2584,$R_A=R_f$ +2585,$\mathsf{VaR}_p(X)=q^-(p)$ +2586,$E(u(X)) \le E(u(Y))$ +2587,$(\beta_i g(S))'(x)=-\mathsf E[X_i\mid X=x]g'(S(x))f(x)/x=-\kappa_i(x)g'(S(x))f(x) / x$ +2588,$a \ge 1$ +2589,"$\mathsf{biTVaR}_{0,p}^w(X)$" +2590,$\iota^\ast = (g(s^\ast)-s^\ast) / (1 - g(s^\ast))$ +2591,$g'(s)\ge 0$ +2592,"$X:\Omega\to [0,\infty]$" +2593,"$\mathsf{TVaR}_{0.95}(X)=\int_0^{1000}g(S(x))\,dx$" +2594,$\rho(X_n)\to \rho(X)$ +2595,$\lambda_{obj}$ +2596,$W_0$ +2597,$0=q(0)=q(Y+(-Y))\le q(Y) + q(-Y)$ +2598,$cv=0.287$ +2599,$g_\tau(0)=0$ +2600,$0.41$ +2601,$\mathsf P(X=q_X(p))>0$ +2602,$p=0.8$ +2603,$\kappa_1(10)$ +2604,$\mathsf E_\mathsf{Q}[X_i(a)]$ +2605,$\mathsf E[(X-\mathsf E X)^+]$ +2606,"$[0,p)$" +2607,$a_1'$ +2608,$S(x)=1-\Phi((x-\mu)/\sigma)=\Phi(-(x-\mu)/\sigma)$ +2609,$X_{t+1}$ +2610,$X=0$ +2611,$p\mapsto g(1-p)$ +2612,$\downarrow$ +2613,$X\wedge 20$ +2614,$\mathsf{TVaR}_1( X )$ +2615,"$x_1, x_2$" +2616,$\bar P_{2}$ +2617,$\Sigma$ +2618,$B\subset A$ +2619,$\bar P=\mathsf{TVaR}_{p^\ast}(X)$ +2620,$\bar P^a_g(X_i\subseteq X)$ +2621,"$\mathcal{M} = \{ f \mid \|f\|_q\le c, f\ge 0 \}$" +2622,$X \preceq_m Y$ +2623,"$\mathsf E[X_i(a)\,g'(S_{X\wedge a}(X\wedge a))]$" +2624,$qX_i$ +2625,$X \prec_n Y$ +2626,$X(\omega)\Pr(\omega)$ +2627,$\bar\iota=0.10$ +2628,$a=18000.0$ +2629,$\mathsf{TVaR}_{0.95}(X)=1000$ +2630,$s_0/2^{n+1}$ +2631,$\delta(x)$ +2632,$H[X]$ +2633,$\rho(X_0+Y) \ge \rho(X_0) + \mathsf E[YZ]$ +2634,"$x_1,x_2$" +2635,$>100$ +2636,$dh - h_x dx = (r_h-\mu_L)(h-h_x x)dt$ +2637,$\alpha<1$ +2638,$2.576\times 6.258$ +2639,$\mathsf{TVaR}_{p*}(X)=a$ +2640,$\kappa_i(X) = X_i$ +2641,$a_i = a(X_i; X)$ +2642,$\rho(X_n(t))+t\pi$ +2643,$\mathsf{TVaR}_{p}$ +2644,$g(A)/p=59.142$ +2645,$Z(S_X(x))=-(x-\mu)/\sigma$ +2646,$\nu=1-\delta$ +2647,$\{\omega\in\Omega\mid X(\omega)\le x\}$ +2648,$X_n= X_g-X_c$ +2649,$s^*$ +2650,$\bar P_{0}$ +2651,$X\wedge 30$ +2652,$k+1/2$ +2653,$\mathsf{CTE}_{p_0}=\mathsf E[X \mid X \ge x_0]$ +2654,$\lambda=5$ +2655,$D_3$ +2656,$\ge c$ +2657,$\kappa_i(X)$ +2658,$L(X)=w(X)/\mathsf E[w(X)]$ +2659,"$\mathsf{PH,SA,CX}$" +2660,$\phi:=\rho\circ F$ +2661,$u_j(x) = 1 - exp(-\lambda_j x)$ +2662,$\mathsf E[X]+\var(X)/\mathsf E[X]$ +2663,$M_{1}$ +2664,$\mathsf E[YZ_\epsilon]\to\mathsf E[YZ]$ +2665,$X-V$ +2666,"$\bar P_i = \sum_{j} X_{i,j}\Delta g(S_j)$" +2667,$f(t)$ +2668,"$[0, \epsilon_1]$" +2669,$\pi=1$ +2670,$\psi(0)=1-\Pr(Y=0)=1-\Pr(M=0)=\frac{1}{1+r}$ +2671,$a_l \le 1$ +2672,$P_g\not\ll P_X$ +2673,$\delta_i=\delta$ +2674,$p_Y>0.5$ +2675,$-g'(1-p)<0$ +2676,$\rho(X+Y) = \rho(X) + \rho(Y)$ +2677,"$(0.5,1]$" +2678,$F(x_0)=p_+$ +2679,"$(X_i, X)$" +2680,$\mathsf E[X]=\mathsf{TVaR}_0(X)$ +2681,$l(kX)=k\rho(X)$ +2682,$\int udv = uv - \int vdu$ +2683,$r_P-\mu_L$ +2684,$\mathsf E[X_i\mid X\le a]F(a) + a\mathsf E[X_i/X\mid X >a]S(a)$ +2685,$\bar P(a)=\displaystyle\int_0^a g(S(x))dx$ +2686,$g(x) = (x-\mu)^2$ +2687,$\mathsf{biTVaR}(Y)=\mathsf{TVaR}_{p^\ast}(Y)$ +2688,$0$ +2689,$p=1-g(1-F(x))$ +2690,$\bar S_i(3463)$ +2691,$X=X(\omega)$ +2692,$\int_0^1$ +2693,$\esssup(X)g(0-)$ +2694,$\mathsf E[X \mid U]$ +2695,$\tilde p$ +2696,$\bar P'$ +2697,$\sum_i E[X_i|anything]\le _{cx} \sum X_i \le_{cx} F_{X_i}^{-1}(U)$ +2698,$\lambda = \lambda_0+\lambda_1$ +2699,$X_{-2}=C_1 + \cdots + C_n$ +2700,$X_{0}$ +2701,$\rho_g = \int g(S)$ +2702,$a={{break_even}}$ +2703,$x=q(1-g^{-1}(1-\tilde p))$ +2704,$0.5\le p^* \le 0.75$ +2705,$X(\omega)=1$ +2706,$P(a)=S(a)+\delta F(a)$ +2707,$\mathsf{TVaR}_{1-c\epsilon}(X) = \mathsf{VaR}_{1-\epsilon}(X)$ +2708,$q(p)=S^{-1}(1-p)$ +2709,$d_i= i/(1+i)$ +2710,$P=\sum_i P_i$ +2711,$B_i$ +2712,$a_1=a(W_1)$ +2713,$\rho=\esssup=\mathsf{TVaR}_1$ +2714,$\sigma(X)^2$ +2715,$g'(s)=1/(1-p)$ +2716,$0.4$ +2717,$f'_+(x)=\lim_{h\downarrow 0} (f(x+h)-f(x))/h$ +2718,$g'(1)=1$ +2719,$\mathcal Q_1$ +2720,$X\le m$ +2721,$\mathsf E_\mathsf{Q_k}[X_j]$ +2722,$\mathbf{\min a}$ +2723,$dt^2$ +2724,$q=p$ +2725,$\sigma_d = \mu_d/5$ +2726,$\mathsf E[cZ]=c\mathsf E[Z]=c$ +2727,$\mathsf E[(X-\mu)^2]$ +2728,$Q_0$ +2729,$X_t=X_{t+1}$ +2730,$g(s)=0.1995$ +2731,$\log(0)=-\infty$ +2732,$\mathsf{VaR}_p(X_1)$ +2733,$W_t$ +2734,$Z_{\tilde X}$ +2735,$U0$ +2748,"$\{4,5\}$" +2749,$h(x)=f(x)/S(x)$ +2750,$S\Delta X\wedge a$ +2751,$r_U$ +2752,$\mathsf E_\mathbb{Q}[X]$ +2753,$\mathsf E[X_d]$ +2754,$(c(S\cup \{i\})-c(S))$ +2755,$\mu(dp)=f(p)dp$ +2756,$X\preceq_2 Y$ +2757,$P \le \dfrac{S}{\lambda} \approx \dfrac{\mathsf E[X]}{\lambda}$ +2758,$v(E)$ +2759,$\{Z\circ T\mid T:\Omega\to\Omega\text{\ PPT}\}$ +2760,$\mathsf E[X_ih(X)]$ +2761,$S(x_i-)-S(x_i) =\Pr(X=x_i)$ +2762,$6/6$ +2763,$\Phi(\Phi^{-1}(s) + \lambda)$ +2764,"$[0, -k]$" +2765,$\mathcal E(X)=c\mathsf E[X^2]$ +2766,$\mathsf P(X=\mathsf{VaR}_p(X))>0$ +2767,$\mathsf E[X] = \displaystyle\int_\Omega X(\omega)\Pr(d\omega)$ +2768,$\rho(W_0\wedge a_0)=\bar P_0 +\bar P'$ +2769,$U(t)$ +2770,$p=1-s$ +2771,"$\sum_i a(X_i, p^*)=a$" +2772,$q_{X_1}(p)+q_{X_2}(p)=q_{X_1+X_2}(p)$ +2773,$8.5$ +2774,$\mathbf{\Omega}$ +2775,$M_{1}\Delta X$ +2776,$\bar P_i(a)$ +2777,$T_i$ +2778,$L_0^y$ +2779,$2$ +2780,$\rho(c)=\rho(0+c)=\rho(0)+c$ +2781,$U_X(\omega)=F(X(\omega)-) + V(\omega)(F(X(\omega)) - F(X(\omega)-))$ +2782,$s = 1-10^{-15}$ +2783,$s/g(s)$ +2784,$\alpha f$ +2785,$\{\omega\in\Omega \mid X(\omega)=x\}$ +2786,"$[0,1]$" +2787,$a(\mathbf{v})=\mathsf{TVaR}_p(\mathbf{v})=\mathsf E[X\mid X > q_{\mathbf{v}}(p)]$ +2788,$M=\varnothing$ +2789,$1/(1-p)$ +2790,"$(0,0),\ (1,0),\ (1,1)$" +2791,$t\mapsto \rho(X) + t\mathsf E_{\mathsf Q_X}[Y]$ +2792,$\omega_i\in B$ +2793,$g'(1)=\alpha$ +2794,$\le 1$ +2795,$-\rho(-X)$ +2796,$g(S(x_i-))-g(S(x_{i-1}))$ +2797,$f_{opt} = 1-s/g$ +2798,$\Delta \mathit{MV}_{ro}(a)$ +2799,$Q_i=a_i-P_i$ +2800,$0.0476/(1-0.0476)=0.05$ +2801,$q=0.9215$ +2802,$f(x)dx$ +2803,$\mathcal F'$ +2804,$\nu (1-s)$ +2805,$p=\Phi((a-\mu)/\sigma)$ +2806,$g'(1-s)$ +2807,$\Pr({\omega})=1/6$ +2808,$P(X_{-1}\wedge a_{ro})=9196.39$ +2809,$\omega_0$ +2810,$g_2(s) = 2s/3 + 1/3$ +2811,$\bar S(a):= \mathsf E[L_0^a(X)]=\mathsf E[X\wedge a]$ +2812,$x^\ast$ +2813,$2/3$ +2814,$\iota(s)=w/(1-w)$ +2815,$\phi(0)=0$ +2816,$\log(S) =\mu t$ +2817,$a\le (P(1+\iota)-S)/\iota$ +2818,$g'(s_1) \ge (1-g(s_1))/(1-s_1)$ +2819,"$U, V$" +2820,$s^{0.642}$ +2821,$\kappa_i(x)=mx/(m+n)$ +2822,$C\mathsf X$ +2823,$s_0=1$ +2824,"$\Omega=\{1,2\}$" +2825,$\min_{\eta\in \mathbb{R}} \eta + \alpha \mathsf E[(X-\eta)^+] -\beta\mathsf E](X-\eta)^-]$ +2826,$X\mapsto\int X(\omega)Z(\omega)\mathsf(d\omega)$ +2827,$\rho(X_0+\epsilon Y)-\rho(X_0)$ +2828,"$\sigma_A,\sigma_L$" +2829,$P(a)=g(S_X(a))$ +2830,$Z_\epsilon\to Z$ +2831,$\alpha_i(x) =\mathsf E[X_i/X\mid X>x]$ +2832,$a\beta_1g(S)$ +2833,"$\mathsf{biTVaR}_{p,1}^w$" +2834,"$(s^\ast, g(s^\ast))$" +2835,$a^\star$ +2836,$\mathsf E_{\mathsf Q}[\cdot]$ +2837,$\mathsf E[X_i\mid \{X=X(\omega)\}]$ +2838,$\beta_i(x)$ +2839,"$\mathbf{S\,\Delta X}$" +2840,$\rho(X+tY)\ge \mathsf E_{\mathsf Q_X}[X+tY]=\mathsf E_{\mathsf Q_X}[X]+\mathsf E_{\mathsf Q_X}[tY]=\rho(X)+t\mathsf E_{\mathsf Q_X}[Y]$ +2841,$\mathsf EPD_s(X)$ +2842,$\rho(X)=1.169$ +2843,$S(a)=\mathsf E[1_{X>a}]$ +2844,$U(\omega)=\omega$ +2845,${X}$ +2846,$D^f\rho_{X;\tilde X}(X_i)$ +2847,"$d(g(S(x)))/dx=-g'(S(x))\,dF/dx$" +2848,$S(x+a)$ +2849,$\rho(0)=0$ +2850,$\succeq^2$ +2851,$\mathsf E_{\mathsf Q}[Y] = \mathsf E[Yg'(S_X(X))]$ +2852,$a=\mathsf E[X \mid X > q(p)]$ +2853,$\mathbf{Q_1\Delta X}$ +2854,$\rho(\lambda X)=\lambda \rho(X)$ +2855,$q(p) \times \phi(p)dp$ +2856,$E(X_{-1}(a))=\bar S_0(a)$ +2857,$X\mapsto \mathsf E[XZ]$ +2858,$q_2(t)=t^2$ +2859,$\sigma^2=\sigma_A^2 + \sigma_L^2 - 2\rho\sigma_A\sigma_L$ +2860,"$(0.5, 0.5)$" +2861,$a_lp}$ +2881,$\int X=0$ +2882,$\mathsf{j}(0)=0$ +2883,$g'(S(x))>1$ +2884,$0<\alpha\le 1$ +2885,$-q(-Y)$ +2886,$X_c$ +2887,$r_f /(1+ r_f)$ +2888,"$[1,\infty)$" +2889,$4.75$ +2890,$D_c$ +2891,"$X_{t-2,1}$" +2892,$L\mathsf{VaR}_p(X)}$ +2904,$\gamma(ds)$ +2905,$Z=20\cdot1_A$ +2906,$X_n(\omega)= 1$ +2907,$\mathsf{Var}(X)$ +2908,$\bar M_t = \bar P_t - \mathsf E[Y_{t}]$ +2909,$f=(1-p)^{-1}1_{W}$ +2910,$\rho(X_n)=0$ +2911,$1_{X\le a}$ +2912,$af\le 1$ +2913,$ for estimates $ +2914,$X+W$ +2915,$X=\mathsf E[Y \mid \mathcal F']$ +2916,$\mathsf E[(-Y)Z]\ge 0$ +2917,$gS$ +2918,$\Delta X_7$ +2919,$Z=\tilde X_2$ +2920,$a\alpha_i(a)=\kappa_i(a)$ +2921,$B-p(\nu(p) + il(p))$ +2922,"$(0,0,0,0,0,0,5,0,0,5)$" +2923,$\mathsf{VaR}_p(X)=q_X^{-}(p) = \sup \{ x\mid F_X(x) < p \}$ +2924,$\lambda\mathsf E[X]$ +2925,$\omega\in\Omega$ +2926,$g=0$ +2927,$L_0^a$ +2928,$-5.91$ +2929,$X_i=\mathsf E[X_i\mid X]$ +2930,$\bar q_{X_1+X_2}(s)=q_{X_1+X_2}(1-s)$ +2931,$\Pi=B-p\nu(p)$ +2932,"$Y_{2,1}$" +2933,$\rho(X)=\mathsf E_{\mathsf Q_X}[X]$ +2934,$U(a)=-s$ +2935,$\rho(X+Y) = \rho(\lambda(X/\lambda) + (1-\lambda)(Y/(1-\lambda))))$ +2936,$P(x)$ +2937,$r=(1+\bar\iota)/(1+\tau)-1$ +2938,$\mathbf{d=2}$ +2939,$\mathbf{x_2}$ +2940,$\rho(-X)=-\rho(X)$ +2941,$R_L=-k R_f + \beta_L(R_M-R_f)$ +2942,$g(t)$ +2943,$N := \lceil (1-p)M \rceil$ +2944,$\{2\}$ +2945,"$(\nu,\delta)$" +2946,$p\to\infty$ +2947,$1\le\lambda$ +2948,$\rho E/(1-\tau) - rA$ +2949,$\mathbf{\beta_{2}g(S)\Delta X}$ +2950,$x\mapsto x^{1/2}$ +2951,"$j=0,\dots,m=8$" +2952,$\beta_i(a)/\alpha_i(a) > 1$ +2953,$=\displaystyle\int_0^\infty x f(x)dx$ +2954,$a_l-1<0$ +2955,"$\mathcal F'=\{\varnothing, \Omega \}$" +2956,$F_Y^{-1}(V)=q_Y(V)$ +2957,$Z_{\mathit{lin}}$ +2958,$0\le p_0\le p^*\le p_1\le 1$ +2959,$log(x)$ +2960,$\mathsf{TVaR}_0( X )=\mathsf E[X]$ +2961,$\nu=\nu(a)<1$ +2962,$X_1$ +2963,$X(\cdot)$ +2964,"$Z=(0,0,0,0,0,0,0,0,5,5)$" +2965,$Z_{\mathit{lift}}$ +2966,"$\mathbf{B}:\left [0,1 \right ] \ni t \mapsto (x(t),y(t)) \in \mathbb{R}^2$" +2967,"$(\Omega, P)$" +2968,$0 \le p<1$ +2969,$\mathbf{\Delta X}$ +2970,$\mathsf Q_X$ +2971,$1_A/\Pr(A)$ +2972,$n < N-1$ +2973,$\bar P(x)=\int_0^x P(t)dt$ +2974,$F(x_0)\ge p$ +2975,$X-a$ +2976,$\alpha_i(a)S(a)=\mathsf E[(X_i/X)1_{X>a}]$ +2977,$Z\not=0$ +2978,$\mathsf E X +\lambda_1 {(X-\lambda_2 \mathsf E X)^+}_1$ +2979,$\sigma(Z)=\sqrt{\var(Z)}$ +2980,$\rho(\cdot)$ +2981,$p = (1-s)$ +2982,$p=0.417$ +2983,$(j)$ +2984,"$\int_{[0,1]}$" +2985,$y^{\ast}:=\min(y)$ +2986,$\mathsf E[X]=1/\beta$ +2987,$\mathsf E[X_i (X\wedge a)/X]$ +2988,"$ (MA.south)+(0, -1) $" +2989,$q^-(U(\omega))$ +2990,$Q_2\Delta X$ +2991,"$\mu=0.1, \sigma=0.15$" +2992,$\mathsf E[X_2Z]$ +2993,$P_X(dx)$ +2994,$Y_{2}$ +2995,$Q_1dX$ +2996,${}^nS_X(t)\le {}^nS_Y(t)$ +2997,$(0.5)(20)+(0.5)(30)=25$ +2998,$\rho(X)\not=\sum_i\rho(X_i)$ +2999,"$M\subset \{1,\dots, n\}\setminus \{i, j\}$" +3000,$u(x)=(1-e^{-\pi x})/\pi$ +3001,$\Pr(p(\omega)=0)=0$ +3002,$55+0.675\times 3.807=57.572$ +3003,$D \rho(X_0)$ +3004,$\alpha(1-f)$ +3005,$90$ +3006,$L_{250}^{\infty}(x)$ +3007,$q(1)=\infty$ +3008,"$(p,q(p))$" +3009,$\prec_2^*$ +3010,$1/r$ +3011,"$\mathbf{v}=(v_1,\ldots,v_n)$" +3012,$\rho(X+X_i)=\rho(X)+\rho(X_i)$ +3013,$\displaystyle\int$ +3014,$\alpha_i(x)<\kappa_i(x)/x$ +3015,$\Pr(X_n=1)=1/n$ +3016,"$\{1,2,3,4,5,6\}$" +3017,"$(X_1,\dots, X_n)'$" +3018,$1_A(x)=0$ +3019,$X_{-4}=x$ +3020,$\mu-\sigma^2/2$ +3021,$s(1)=s_3=1$ +3022,$g(x)=0$ +3023,$L_0^{a+y}=L_0^a+L_a^{a+y}$ +3024,$x_{#4}$ +3025,$n\ge 1$ +3026,$2.576$ +3027,$Q_j=1-g(S_j)$ +3028,"$B_2=[0,0]$" +3029,$\sum c_i^2$ +3030,$\mathsf E[X_1\mid X=x]$ +3031,$X_i(v_i)$ +3032,$\alpha_i(a)S(a)$ +3033,$X(\omega)=0$ +3034,$U \ge U_s$ +3035,$g_i$ +3036,$\lambda=(1-\alpha_p)^{-1}$ +3037,$\bar P = a - \bar Q$ +3038,$p(1-\nu(p)-il(p))$ +3039,$Z_{a}(x)=g(S_X(a))/S_X(a))$ +3040,$X(\omega_1)a'$ +3042,"$0.1, 0.4, 0.5,\dots, 0.9$" +3043,"$I(q,p) \ne I(p,q)$" +3044,$k=-\log(p)/u$ +3045,$S(x_{i-1})-S(x_{i})=S(x_i-(x_i-x_{i-1}))-S(x_i)=-S'(x'_i)(x_i-x_{i-1})=f(x'_i)(x_{i}-x_{i-1})$ +3046,"$x,y\in C$" +3047,$g^{-1}(x)\le s$ +3048,$f(x) < f(y)$ +3049,$\iota^{\star}$ +3050,$(1+\rho)\mathsf E[C]$ +3051,$Z(\omega)=\dfrac{1}{1+r}\dfrac{\mathsf Q(\omega)}{\mathsf{P}(\omega)}$ +3052,$\zeta_{s} = \Phi^{- 1}(s)$ +3053,$\displaystyle\int_\Omega X(\omega)p(\omega)\Pr(d\omega)$ +3054,$\iota$ +3055,$\rho \ge \mathsf E[X]$ +3056,$d^* = D/L^*$ +3057,$\mathbf{K}$ +3058,"$\rho(X) = \max\{\rho_c(X), \mathsf{TVaR}_{0.8}(X) \}$" +3059,$S(x)=1$ +3060,$g(s)=\Phi(\Phi^{-1}(s)+\lambda)$ +3061,$\mathbf r$ +3062,$\rho_g(X)<\infty$ +3063,$M=\iota Q$ +3064,$\mathcal D(X)+\mathsf E[X]$ +3065,$q + 2pq + 3p^2q+\cdots=q(1+2p+3p^2+\cdots)=1/q$ +3066,$g'(1-p^* )=1$ +3067,$-1$ +3068,$\Pr(X< q(p))\le p \le \Pr(X\le q(p))$ +3069,"$ In general, define $" +3070,"$(4,2)$" +3071,$\alpha=1$ +3072,$\alpha_{Cat} \le \beta_{Cat}$ +3073,$R_S$ +3074,$dt$ +3075,$E_i\in\mathcal F$ +3076,"$\bar P_{0,0}:=\rho(Y_{0,0})$" +3077,$\mathcal V(X)=\mathsf E[X]+c\mathsf E[X^2]$ +3078,$a_1 < a_0-X_1$ +3079,$\mathsf E[X]=28$ +3080,$ is different from the contact function $ +3081,$t < 2/3$ +3082,"$\omega\in[0,1]$" +3083,"$h(x):=H(x, 1, t)$" +3084,$g(s)=3s$ +3085,$p=0.5$ +3086,"$\lambda\rho(X) + (1-\lambda)\rho(Y) \le \max(\rho(X),\rho(Y))$" +3087,$\{n_s\}$ +3088,$S(X_0)$ +3089,$r_m$ +3090,$X_i=X_i(a)$ +3091,$\mathsf{CTE}_p(X) := \mathsf E[X \mid X \ge \mathsf{VaR}_p(X)]$ +3092,$\bar Q_{act} = \bar Q - F_0$ +3093,$\beta_i/\alpha_i$ +3094,$\bar P(a)= (1-e^{-a\alpha\beta})/(\alpha\beta)$ +3095,$S(x)=e^{-x/\mu}$ +3096,$\mathsf E[Xe^{\pi Z}]/\mathsf E[e^{\pi Z}]$ +3097,$M(x)/(1-S(x))$ +3098,$\Pr(Xq_X(p)}$ +3105,$d(g(S(x))/dx=g'(S(x))f(x)$ +3106,$p={{p}}$ +3107,$\rho(X) = \mathsf E[X] + c\mathsf E[X-\mathsf E[X]]^+$ +3108,$v\in V$ +3109,$\iota=0.10$ +3110,$\hat p > p$ +3111,"$C(S_0, a, t)$" +3112,$c = 0.5(0.5)2.5$ +3113,$M = 0.603$ +3114,$\Pr(A\cup B)=\Pr(A)+\Pr(B)$ +3115,$A/(A-P)$ +3116,"$A,B,C,D$" +3117,$h=\sin(77 s)$ +3118,$\sup \{ \mathsf E[X\mid A] \mid \Pr(A) > 1-p) \}$ +3119,"$\mathbf{X\,p}$" +3120,$g(s)=1-(1-s)^3$ +3121,$\phi\in \mathcal E$ +3122,$F_1 \prec_1 F_0$ +3123,$\lim_{s \downarrow 0}1/g'(s)$ +3124,$\Delta_j =g'(s_j-)-g'(s_j+)=\phi((1-s_j)+)-\phi((1-s_j)-)$ +3125,$\Omega_0:=\{\omega\in \Omega\mid X(\omega)=\max(X)\}$ +3126,$f(s)\le s$ +3127,$\bar\iota(a)$ +3128,$j>0$ +3129,$n=1$ +3130,$S_0$ +3131,$g(S(x))=g(S(x-))=1$ +3132,$A\subset\mathbb{R}$ +3133,$f(p)=(1-p)\phi'(p)=-(1-p)g''(1-p)$ +3134,$ then $ +3135,$\epsilon_1$ +3136,$i>0$ +3137,"$0, 1, 90$" +3138,$\beta_1<\alpha_1$ +3139,$\nu p$ +3140,"$n=1, p=1/{{p}}={{pf}}$" +3141,$q(U)=F^{-1}(U)$ +3142,$\sqrt{0.1}=0.316$ +3143,$\ge 0.95$ +3144,$vL + da$ +3145,$g'(s)=\nu$ +3146,$b=0.5$ +3147,$\mathbf{x_1}$ +3148,$a < b_h$ +3149,$L>d$ +3150,"$a_{0,2}$" +3151,$a_i=a(X_i; X)$ +3152,$\mathsf E_F(h(X))$ +3153,$\dot f(t)=a(x)$ +3154,$A^c$ +3155,"$\mathsf P((a,b])=b-a$" +3156,$1-p$ +3157,$\lim_{s \downarrow 0} s/g(s) = \lim_{s \downarrow 0}1/g'(s)$ +3158,$\rho_\mu$ +3159,$\bar F(a)$ +3160,$P(X_{0}(a_{gc}))$ +3161,$\mathbf{\alpha_2}$ +3162,$20+8t>20+10t$ +3163,$b=1$ +3164,$p_0 = p^\ast = p_1$ +3165,$Z\in L^1$ +3166,$Y$ +3167,$g(S(x))=u$ +3168,$\phi'(s)\ge 0$ +3169,$x\mapsto (x-d)_+^{n}$ +3170,$\{X \le x^*\}$ +3171,$\mathbf{M_1\Delta X}$ +3172,"$X_1=0,0,0,0,1,1,2,3,20, 400$" +3173,$\mathsf E[XZ]$ +3174,$m_1=m_2$ +3175,"$\dfrac{\partial\rho}{\partial P} = \dfrac{0.4^2 P}{\rho(P,R,a)}$" +3176,$u = g(S(x))$ +3177,$\mathsf E[\mathsf E[Z\mid X]]=\mathsf E[Z]$ +3178,$\rho(X)=g(q)$ +3179,$\bar M=\bar P-\bar S$ +3180,$\mathsf E[Z\mid X]=0$ +3181,$\mathbf{s_1}$ +3182,$q_Y(1-U)$ +3183,$h(s)$ +3184,$f^{-1}(A)\in\mathcal B$ +3185,$\beta_1g-\alpha_1S$ +3186,$X_2(a)$ +3187,$g'(s)=bs^{b-1}$ +3188,$\mathsf P(A)=1-p$ +3189,$dF(x)$ +3190,"$(0,g_0)$" +3191,$\kappa_1(X)$ +3192,$x \mapsto -x$ +3193,$A(1_{X>x_1} + 1_{X>x_2})= A(1_{X>x_1}) + A(1_{X>x_2})$ +3194,${Z}_p \le c$ +3195,$X:\Omega\to\mathbb{R}$ +3196,$C_1+\cdots + C_n$ +3197,$0=\Pr(X<1)<\Pr(X\le 1)=1/6$ +3198,$\rho(X)=\mathsf E[XZ]$ +3199,$\tilde X\wedge a$ +3200,$d+v=1$ +3201,"$\Omega=[0,1]$" +3202,$q_Y$ +3203,$D\rho_X(\cdot)$ +3204,$g^{-1}(u)$ +3205,$\sum_{i}X_{i} = X$ +3206,$g_{ROE}$ +3207,$>1-p$ +3208,$a=\mathsf{VaR}_{1-\tau}(X)$ +3209,$h(x):=f(x)/S(x)$ +3210,$X_n(\omega)=1$ +3211,$\mathbb{R}$ +3212,$S_Y$ +3213,$\chi^2$ +3214,$X=X' + X''$ +3215,$(X\wedge a)\Delta g$ +3216,$f(x)\approx 0$ +3217,$ but if $ +3218,$Q=(a-EL)/(1+r)$ +3219,$\max_{\mathsf{Q}} \mathsf E_\mathsf{Q}[0] -\alpha(\mathsf Q) =\max_{\mathsf{Q}} -\alpha(\mathsf Q)= -\min_{\mathsf{Q}} \alpha(\mathsf Q) = 0$ +3220,$a\ge 0$ +3221,$\mathbf{F}$ +3222,$N=5$ +3223,$\{ X=x \}$ +3224,"$D_n,D_n^*$" +3225,$X_d$ +3226,$Z=\mathsf E Z$ +3227,$\rho_g(X)=\mathsf E_{\mathsf{Q}}[X]$ +3228,$P=g(s)$ +3229,$\int xdF(x)=\int xf(x)dx$ +3230,$\mathsf E[X] = \mathsf E[\mathsf E[X\mid Y]]$ +3231,$X({\mathbf{v}})$ +3232,$g(s)=s^{0.9}$ +3233,"$X_{t,1}$" +3234,$x=X(p)$ +3235,$\mathsf E[X_i(a)]$ +3236,$\mathsf E[1_{U_X\ge p}]=\mathsf E[B]$ +3237,$\hat s$ +3238,$\mathsf E X + c{ X-MX }$ +3239,$\sigma_i^2$ +3240,"$(1-s, 1-g(s))$" +3241,$\ge$ +3242,$h(p)$ +3243,$\max(X)=1$ +3244,$R_f$ +3245,$\mathbf{X_1}$ +3246,$\phi(s)=0$ +3247,$P = \mathsf E[X] + \pi \mathsf{Var}(X)$ +3248,$\mathsf{Var}(X+c)=\mathsf{Var}(X)$ +3249,$\mathsf{TVaR}_{0.975}$ +3250,$l^\infty$ +3251,$\mathsf E[Yg'(S(X))]$ +3252,$x_p=\mathsf{VaR}_p(X)$ +3253,$\sum v_iX_i$ +3254,$R$ +3255,$s=0.5$ +3256,"$(1-S(x),x)=(p,q(p))$" +3257,$0!=1$ +3258,$\rho(U)=1$ +3259,$x=1000$ +3260,$m(1)=0$ +3261,$a_{t} = a_{t-1}$ +3262,$A=\{X(\omega) > x\}$ +3263,$\beta_i(a)g(S(a))=\mathsf E_{\mathsf{Q}}[(X_i/X) 1_{X>a}]$ +3264,$\mathsf E[X\wedge a(X)]$ +3265,$0.1 < s < 0.2$ +3266,$p < 1$ +3267,$g(0+)\ge 0$ +3268,"$3.129=\lambda \sigma(Y_{0,0})$" +3269,$\mathsf E[X\mid \mathcal F_t](\omega)$ +3270,$\beta_i(x)/\alpha_i(x)> 1 > S(x) / g(S(x))$ +3271,$S(x)\approx k x^\alpha$ +3272,"$\mathit{EGL}_{gc}(a)>\max(0, \mathit{EGL}_{ro}(a))$" +3273,$\alpha_1(99)=0.1$ +3274,$\mathsf{TVaR}_p(X)=80$ +3275,$m\ge n$ +3276,$(a-X)^+$ +3277,$M_1dX$ +3278,$(X\wedge l)(\omega)=X(\omega)\wedge l$ +3279,$a=a[X]$ +3280,$\mathbf{a_{2}}'$ +3281,$a^{\star}(X)-a(X)$ +3282,$\mathit{PV}_{r_X}(X) + \mathit{PV}_{r_f}(\text{UW profit tax})$ +3283,$A-A\Phi(d^*)=A\Phi(-d^*)$ +3284,$\Pr(\varnothing) =0$ +3285,"$j=0,\dots, m-1$" +3286,$n\Pr(Y\le y_c)$ +3287,$(P-S)/(a-P)\ge \iota$ +3288,$(1-p)^{-1} \min_x x(1-p) + \mathsf E[(X-x)^+]$ +3289,$r^*$ +3290,$F(x)=\P(X\le x)$ +3291,$\bar Q(x)$ +3292,$q^-(p)=\sup\ \{ x\mid \Pr(X < x) < p \}$ +3293,"$(a,b] \subset [0,1]$" +3294,$\mathsf E[X_iX]$ +3295,$\mathbf{s}$ +3296,$\rho(X_0) = \mathsf E[X_0Z]$ +3297,$\iff$ +3298,$\exp$ +3299,$\mathbf{1_{X>x}}$ +3300,$D>L$ +3301,"$\mathsf{biTVaR}_{0,1}^{0.0476}$" +3302,$\iota(0.5)=\iota^{\star}$ +3303,$\kappa_{2}$ +3304,$n \ge 1$ +3305,$Y\in L^\infty$ +3306,$\lim_{s \to 1}{\mathsf E[ r_{s} ] = - 1}$ +3307,$0 \ge \rho(-X+a)=\rho(-X) + a \ge -\rho(X) +a$ +3308,$\mathsf E[XZ]=\mathsf E[X\mathsf E[Z\mid X]]=0$ +3309,$a>0$ +3310,$\mathbf{X_2}$ +3311,$1\le p \le \infty$ +3312,$\mathit{PFL}$ +3313,$X_i(a)=X_i\dfrac{X\wedge a}{X}$ +3314,$\mathbf\Omega$ +3315,$g'(1)$ +3316,$0\le \alpha\le 1$ +3317,$g(S(x))=0$ +3318,$\rho\ge 0$ +3319,$\nu(p)=1/(1+\iota(p))$ +3320,"$[0,\infty)$" +3321,$\uparrow$ +3322,$a_i + b_i\ \mathit{EL}$ +3323,$\mu t + \sigma dW_t -\sigma^2 dt /2 +o(dt)$ +3324,$h$ +3325,$4/6$ +3326,$X_2=c_2+2Y$ +3327,$-Y\ge 0$ +3328,$S(x_2)(x_3-x_2)$ +3329,$0\le\lambda \le 1$ +3330,$\mathsf E[X_iZ]=\rho_g(X)/2$ +3331,$x \ge x^\ast$ +3332,$1/4 < s\le 1$ +3333,$A_X = 5.976$ +3334,$\rho(X+Y)\ge$ +3335,$\mathbb{Q}(\Omega_a) >0$ +3336,$\mathbf{t+2}$ +3337,$M = r K$ +3338,$X_n(\omega)=n$ +3339,$r = 0.6565$ +3340,$\nu^{\star}$ +3341,$-\rho(-X) =b-\rho(b-X)$ +3342,$\mathsf E_{\mathsf{Q}}[Y\mid X]\mathsf E[Z\mid X] = \mathsf E[YZ \mid X]$ +3343,$\alpha_1SdX$ +3344,"$a(\cdot, p)$" +3345,$\tau \ge t+d$ +3346,$\mathsf E[u(P-X)]=0$ +3347,$\mathsf E[X_1]=4.75$ +3348,$\mathbf{Q}$ +3349,$\mu(\{p\})=1$ +3350,$c\approx -\sigma^2u''(w)/u'(w)$ +3351,$X\wedge a=\sum X_i(a)$ +3352,$\rho(X)\ge\rho(X+Y)\ge \rho(X)+\mathsf E[YZ]$ +3353,$\mathbf{M\Delta X}$ +3354,$\mathsf E[XB]$ +3355,$\kappa_i(x)=E[X_i \mid X=x]$ +3356,$\lambda_0$ +3357,$\epsilon /2^{n+1}$ +3358,$\nu(x)$ +3359,$S(x)=\exp(-\int_x^\infty h(t)dt)$ +3360,$g(P)$ +3361,$2x$ +3362,$P(a) = g(S(a))$ +3363,$[F(x)](\cdot)$ +3364,"$\Omega=\{\omega_1, \ldots, \omega_6\}$" +3365,$\mu-\sigma^2/2=0.0992$ +3366,$F(p)=0.6$ +3367,$\rho(X_j)$ +3368,$\mathbf{M_2\Delta X}$ +3369,$y=a$ +3370,"$\mu,\sigma$" +3371,$g_i=g^{-1}(u_i)$ +3372,$u=0.1$ +3373,$1_{U>s}$ +3374,"$\rho(X)=\int g(S(t))\,dt$" +3375,$S=\mathsf E[X\wedge a]$ +3376,$\{ x \mid F(x) \ge p \}$ +3377,"$\mathsf E_{\mathbb{Q}}[Y]=\mathsf E[Y\,g'(S(X))]$" +3378,$g(s)q$ +3379,$\mathsf{VaR}_1(X)$ +3380,$\sigma_L$ +3381,$\mathsf E[(X-a)^+]/\mathsf E[X]$ +3382,$Q=1-g$ +3383,$L_a^{a+y}(X)$ +3384,$\rho(X)=\mathsf{SD}(X)$ +3385,"$\int_{[a,b]} h(x)dF(x)$" +3386,$\bar\nu(a)=1/(1+\bar\iota(a))$ +3387,$-g''(1-p) = \phi'(p) = (1-p)^{-1}f(p)$ +3388,$g(S_X(X))$ +3389,"$(\Omega, \mathcal F, \mathsf P)$" +3390,$0\le p\le 1$ +3391,"$D^f\rho_{X\wedge a,X}(\cdot)$" +3392,$P = \mathsf E[X] + \pi \max(X)$ +3393,$\mathbf{g_1(s)=s^{0.4}}$ +3394,$V^{\ast}(1)=p/(1+r-p)$ +3395,$H_k(X)=H_{g_k}(X)$ +3396,$\partial\bar P/ \partial a$ +3397,$f(x)/S(x)$ +3398,"$X_{t,d}$" +3399,$a_{d} = \mathsf E[Y_{d}]+4\sigma(Y_{d})$ +3400,$a=\mathsf E_\mathsf{Q}[X]$ +3401,$\Delta S=0$ +3402,$\mathcal V(X)=\frac{1}{1-p}\mathsf E[X^+]$ +3403,$s_3=1$ +3404,$0< a\le 1$ +3405,$B(1_{X\le x})$ +3406,$2^{-t+1}$ +3407,$\beta < \alpha$ +3408,"$\bar P_i(\mathbf{v},a)$" +3409,$\sum \Delta g(S)_jX_j$ +3410,$\mathsf E X+\lambda\sigma(X)$ +3411,$\rho(0) = \rho(0+0)\le \rho(0)+\rho(0)$ +3412,$a<\infty$ +3413,$X=Y/\lambda$ +3414,$a\alpha_i(a)$ +3415,$q(1-s)$ +3416,$\mathbf{X_{1}}$ +3417,$a_2 = 2.157$ +3418,$\mathsf{TVaR}_p = 20(0.55x_{67}+x_{68}+x_{69}+x_{70})/71$ +3419,$\mathsf{TVaR}$ +3420,$q(\psi)$ +3421,$\mathsf E_\mathsf{Q}[X1_A] / \mathsf E_\mathsf{Q}[1_A]$ +3422,$a_{ro}:=\mathit{VaR}_{p}(X_{-1})={{a_x0}}$ +3423,$( x_{(j)}-x_{(j-1)} )$ +3424,$l(\mathbf X)$ +3425,$p\nu(p)$ +3426,$w_{0.75}$ +3427,$0.7 \ge p < 0.8$ +3428,$\omega_1=1$ +3429,"$(1-g(S(x)),x)=(p,q(1-g^{-1}(1-p))$" +3430,$v=1/(1+\iota)$ +3431,$f$ +3432,$\rho(X)=\mathsf E[h(X)L(X)]$ +3433,$a(X_i)=2.665$ +3434,$\mathsf E[e^{kX}]$ +3435,$\mathbf{B}'(0) = -3\mathbf{P_0}+3\mathbf{P_1}$ +3436,$g_3(s)=s^{0.7}$ +3437,$1-\hat p$ +3438,$P(A\cup B)\le P(A)+P(B)$ +3439,"$(2,-\mathsf x*0.75)$" +3440,$\iff \rho$ +3441,$0\le s\le \epsilon$ +3442,$\rho(X)\le c$ +3443,$X_n(\omega)\to 0$ +3444,$q(p)=25$ +3445,"$(0,3)$" +3446,$g(s)=sv+d$ +3447,$\mathbf{2\mathsf{VaR}_p(X_1)}$ +3448,$a=P+S$ +3449,$\mathsf E[(X-a)^+]$ +3450,"$(x,y)\not=(0,0)$" +3451,$\bar P_0$ +3452,$S=1-F$ +3453,$-t$ +3454,$f(x) = \dfrac{dF}{dx}$ +3455,$-g''(s)=\alpha(1-\alpha)s^{\alpha-2}$ +3456,$\sigma=1$ +3457,$P(a)=1-Q(a)=1-h(F(a))$ +3458,$\delta=\dfrac{\iota}{1+\iota}=\dfrac{M}{a}$ +3459,$s\le s^*$ +3460,"$\mathbf{j, p, S, \kappa_1, \Delta X, \Delta(X\wedge a)}$" +3461,$a' := (1-S)\Delta X$ +3462,$w/s = g'(s-) - g'(s+)$ +3463,$e^{\mu_L}-1$ +3464,$X=m$ +3465,$k(s)$ +3466,$\mathsf Q(A)=\int_A f(\omega)\mathsf P(d\omega)$ +3467,$\Pr(X_n>\epsilon)\to 0$ +3468,$(g-S)dX$ +3469,"$k, b$" +3470,$p^*$ +3471,$\int_0^\infty xf(x)dx$ +3472,$\Delta P$ +3473,$\mathbf{g(S)\Delta X}$ +3474,$r$ +3475,$s+\delta p = 1-\nu p$ +3476,$\mathsf{Var}(\lambda X)=\lambda^2\mathsf{Var}(X)$ +3477,"$m_0, s_1, m_1, s_2, m_2$" +3478,$=\displaystyle\int_0^\infty x \P_X(dx)$ +3479,$\mathit{NPV}_1 = \bar Q - \bar Q_{act} = F_0$ +3480,$\rho_g(X)=35.2$ +3481,$Z=Y-X$ +3482,$\mathsf{TVaR}_{0.642}$ +3483,$g(S(x_B))-g(S(x_B-))$ +3484,$u = \alpha_i(x)S(x)$ +3485,$\alpha_1 < \alpha_2$ +3486,$Z(g(s))=Z(s)+\lambda$ +3487,$\mathit{NPV}_{\infty}=a_xF_0$ +3488,$e^{-kX}/\mathsf E[e^{-kX}]$ +3489,"$X_{1,0}=\cdots=X_{m,0}=X_0=0$" +3490,"$\Omega=\{\omega_1, \omega_2 \}$" +3491,$a(X_i+X_j) < a(X_i)+a(X_j)$ +3492,$m=0.25$ +3493,$\mathbf{M=g(S)-S}$ +3494,$\{Y\mid Y\preceq_2 Z\}$ +3495,"$(de.east |- lee.north)+(0.375,0.25)$" +3496,$c(\{i\})=c(i)$ +3497,$\hat g(s)=1-g(1-s)$ +3498,$W_{s+t}-W_s$ +3499,"$(1,2)$" +3500,$1-s$ +3501,$D_2$ +3502,$x=200$ +3503,$\mathbf{v}$ +3504,"$(0,0,0,0,0,5,0,0,0,5)$" +3505,$P=l + \delta(a-l)$ +3506,$S/L$ +3507,"$\int_0^a F(t)\,dt$" +3508,$\mathbf{X_3}$ +3509,$\int_0^s \mu(dt)/(1-t)$ +3510,$Z\circ T$ +3511,$g(S(a))$ +3512,$\mathsf E[\iota Q] = \mathsf E[\iota]\mathsf E[Q]$ +3513,$\mathcal M_\rho$ +3514,$F(a+)=\lim_{x\downarrow a} F(x)$ +3515,$f<1$ +3516,$\mathcal F_0\times \mathcal F_1$ +3517,$\alpha>1$ +3518,$\rho(Y)$ +3519,$\mathsf E_{\mathsf{Q}}[(X - a)^+] = \rho((X - a)^+)$ +3520,$\mathsf Q(\omega)\ge 0$ +3521,$\lim_{s \uparrow 1}g'(s)$ +3522,$k>2$ +3523,$S\to Y$ +3524,$\Pr(\Omega)=1$ +3525,$s'(t)$ +3526,$g'\circ S_X$ +3527,$s=0.1$ +3528,$g = s/(1-f)$ +3529,$\Delta g(S_j)=g(S_{j-1})-g(S_j)$ +3530,$g(s)=A(1_{U < s})$ +3531,$A\wedge L$ +3532,"$5^{-1},5^{-2},5^{-3},\dots$" +3533,$g'(1-s)+g(0+)\delta_1$ +3534,$+$ +3535,$c(\alpha)x^\alpha g(x)$ +3536,$\mathit{NPV}_{\infty} = a_xF_0$ +3537,$v/\sqrt{n}$ +3538,$X_h$ +3539,"$\mathsf{cov}(X_i,X)$" +3540,"$(p,t)$" +3541,$e^{-rt}S_t$ +3542,$9+1$ +3543,$(x-d)^+ \wedge l$ +3544,$\mathsf Q(B) = \mathsf P(A\cap B)/\mathsf P(A)=\mathsf P(A\cap B)/(1-p_0)$ +3545,$Y_i$ +3546,$\sqrt{x}$ +3547,$\rho(X-X)=\rho(X)+\rho(-X)=0$ +3548,$dG/dF=g'(S(x))$ +3549,$D_m\subset D_n$ +3550,$\mathsf E[X_m\mid X_{m+n}=x]=mx/(m+n)$ +3551,"$[0,1]\subset\mathbb R$" +3552,$r-1$ +3553,$d_f = r_f / (1+r_f)$ +3554,$\hat q(p)=q(1-g(1-p))$ +3555,$X=Y$ +3556,$U^{1/b}$ +3557,$X\preceq_1 Y$ +3558,$E(X-q(X))^+$ +3559,$X_{-2}$ +3560,$t=U_X(s)$ +3561,$3^{30}=2.06\cdot 10^{14}$ +3562,$\rho(kX)\ge k\rho(X)$ +3563,$M(x)=P(x)-S(x)$ +3564,$H$ +3565,$a=\mathsf{VaR}$ +3566,$\int X_n=1$ +3567,"$\displaystyle\int_0^a \kappa_i(x)f(x)\,dx + a\alpha_i(a)S(a)$" +3568,$\alpha_1(90) = (0.0816 \cdot 0.0625 + 0.1 \cdot 0.0625)/(0.0625+0.0625)=0.01135/0.125=0.0908$ +3569,$\mathsf E[X_i\mid X=x]$ +3570,$c_i$ +3571,$0 \le X_i(a) \le X_i$ +3572,$\sup_i f_i$ +3573,$D\rho_X(X_1)=6.2085$ +3574,$+\mathsf{NORIPOFF}$ +3575,"$(a,b)$" +3576,$\mathsf E[g(X_n)]\to \mathsf E[g(x)]$ +3577,$\tilde{\mathbb{Q}}$ +3578,$\mathsf E[X_i(1) \mid X(\mathbf{v}) = q_{\mathbf{v}}(p)]$ +3579,$t\downarrow 0$ +3580,$\mathcal{G}=\sigma(X)$ +3581,$\pi$ +3582,$\mathbf{g_4(s)=s^{0.9}}$ +3583,$h(x)=-d/dx(\log(S(x)))$ +3584,$x=8$ +3585,$X\_{2}$ +3586,$dS$ +3587,$\sum \alpha_i S\Delta (X\wedge a)$ +3588,"$g'(s) = \frac{1-w}{1-p_0}1_{[0, 1-p_0)}(s) + \frac{w}{1-p_1}1_{[0, 1-p_1)}(s)$" +3589,$\mathscr{E}$ +3590,$\Pr(A\le t)= 1/2 + \Pr(U\le t) /2 = 1/2 + t/2$ +3591,$pX$ +3592,$g(S(a))/S(a)$ +3593,$\mathsf E[X\mid \mathcal F'](\omega)$ +3594,$\rho_c(Y)=\mathsf E[Y]$ +3595,$\sum X_i(a)\Delta g(S)$ +3596,"$(p,q(1-g^{-1}(1-p)))$" +3597,$0\le \pi\le 0.5$ +3598,$\bar\delta=\bar\iota/(1+\bar\iota)$ +3599,$q^-(F(x))=x$ +3600,$1-g(s)$ +3601,$P=L + d(a-L)$ +3602,$p\not=0.75$ +3603,"$a=0, b=\alpha$" +3604,$\mathbf{q}$ +3605,$\{ X=\mathsf E[X] \}$ +3606,"$\bar S(a)=\int_0^a S(x)\,dx$" +3607,$X=X\wedge a + (X-a)^+=\sum_i X_i(a) + (X-a)^+$ +3608,$r_f = 0.01$ +3609,$X_2=X-X_1$ +3610,$c_1$ +3611,"$\displaystyle\int_\Omega g(X(\omega), \omega)\Pr(d\omega)$" +3612,$u^{(n-1)}$ +3613,$(r-\sigma^2/2)t$ +3614,$\tau_i=\tau$ +3615,$\tau=\tau_i=0$ +3616,$a=a(s)$ +3617,$f(L)=L$ +3618,$f(L) \le L$ +3619,$p=0.283$ +3620,$g'(s)=\alpha s^\alpha/s$ +3621,$n-4$ +3622,$xdF(x)$ +3623,$\mathsf{TVaR}_{0.8}(X)=25$ +3624,$X_0=X_1=0$ +3625,$Q_X$ +3626,$\mathsf{TVaR}_{p^\ast}(X)=\bar P$ +3627,$P_X(A)=0$ +3628,$L > a$ +3629,$f=0$ +3630,$f(x)dx=dp$ +3631,$P_X(A)=\mathsf P(X\in A)= F(b)-F(a)$ +3632,$Z(a')=g(S_X(a))/S_X(a))$ +3633,"$X_i(\omega), i=1,...,N$" +3634,$\Pr(X\ge x_0)=p_-$ +3635,$v_f(\mathsf E_Q[X_i] - \dfrac{\mathsf E_Q[X_i]}{\mathsf E_Q[X]}\mathsf E_Q[(X-A)^+])$ +3636,$\alpha(\mathsf Q)$ +3637,$\mu(\{p_1\})=w$ +3638,$\phi(p)$ +3639,$\rho(X)=\mathsf E[Xg'(S(X))]=\mathsf E[\sum_i X_i g'(S(X)))]=\sum_i \mathsf E[X_ig'(S(X))]$ +3640,$G\mathsf X$ +3641,$\omega=0$ +3642,$P-D$ +3643,$X>a$ +3644,$\iota=$ +3645,$\lim_{t\to 0}a(X_1; X+tX_1)=a(X_1;X)$ +3646,$e = P/C$ +3647,$\Pr(|X_n(\omega)-X(\omega)|>\epsilon)\to 0$ +3648,$\mathsf E[(a-X)^+]=\int_0^a F(x)dx$ +3649,$t^\star=1/2$ +3650,$t+1$ +3651,$1-B_p=B_{1-p}$ +3652,$\bar M(x)$ +3653,$X\not\preceq_n Y$ +3654,$0\le x < a$ +3655,$\mathsf E[ X_i \mid X(x) = q_{x}(p)]$ +3656,"$Z_2:=\sum_{t+d=2} Y_{t,d}$" +3657,$ since the contact function $ +3658,"$c_1+c_2=(c(1) + c(1,2) - c(2) + c(2) + c(1,2) -c(1))/2=c(1,2)$" +3659,"$(-\infty, \infty)$" +3660,$\Pr(B)=\Pr(A)$ +3661,$\mathsf{Q}(A)=\mathsf E[1_AZ]=0$ +3662,$a(X)\equiv a$ +3663,$x^{**}$ +3664,"$D^f\rho_{X\wedge a,X}(X_i)$" +3665,$X(p)=q(T(p))$ +3666,"$(1-S(x), x)$" +3667,$\tilde X_1+\tilde X_2\succeq^2 \tilde X_1$ +3668,$S_{\mathbf{v}}$ +3669,$\mathsf{VaR}$ +3670,$\bar S_i$ +3671,$\alpha_iSdX$ +3672,$\{X(\mathbf{v}) = q_{\mathbf{v}}(p)\}$ +3673,$c=0.5$ +3674,$K$ +3675,$g(p)/p-1$ +3676,$a(X_i; X)$ +3677,$\log(1+\mu t + \sigma dW_t)=\mu t + \sigma dW_t +o(dt)$ +3678,$\max(X)$ +3679,$x>\sup(X)$ +3680,$M=\inf\{ x\mid S(x)=0\}$ +3681,$\mathsf{VaR}_\pi(X)$ +3682,$\mathbf{\kappa_2}$ +3683,$-k<0$ +3684,$X_n=Y_1+\cdots +Y_n$ +3685,$^{}$ +3686,$\mathsf{CTE}_p(X)=(8+12+25)/3=15$ +3687,$p \ge 0.9$ +3688,$S_0=1000$ +3689,$1_{U0}$" +3707,$\prod_{n\ge N}(1-\frac{1}{n})=0$ +3708,$X\le 0$ +3709,$\mathsf E[1_A]$ +3710,$\rho(W)=\mathsf E[W]+\lambda\sigma(W)$ +3711,$g(s)=s^{0.8}$ +3712,$q \cdot X$ +3713,$p=0.1$ +3714,"$(p, q(1-g^{-1}(1-p)))=(p, q(\hat p))=(p, \hat q(p))$" +3715,$\mathsf P(X\le q_X(p))=p$ +3716,$\mathsf E[e^{X_t}]=e^{\mu t + \sigma^2t /2}$ +3717,"$\rho_1,\rho_2$" +3718,$P/(A-P)=P/Q$ +3719,$-\rho$ +3720,"$\rho_2(X)=\mathsf E[X] + \mathsf{cov}(X,Z)$" +3721,$\alpha_1(98)=0.1$ +3722,$1+2c(1-\Pr(Z>\mathsf E Z))$ +3723,$\pi=1.2613$ +3724,$8+11.1667=19.167$ +3725,$\gamma=0.421$ +3726,$\beta_i(x)/\alpha_i(x) < g(S(x))/S(x)$ +3727,$h(p)=s^3$ +3728,$\psi$ +3729,$f(R) = \mathsf E[f(X)]$ +3730,$\mathsf{VaR}_p(X)=\mu + \sigma \Phi^{-1}(p)$ +3731,$\mathsf E[X_1\tilde Z]=\mathsf E[X_2\tilde Z]=500$ +3732,$B_k$ +3733,"$Binomial(s,N)$" +3734,$x=S^{-1}(g^{-1}(s))$ +3735,$e^{-rt}$ +3736,$\mathsf{VaR}_{p^*}$ +3737,$=\mathrm{MV}(y-T(X))^+$ +3738,$p^{* }$ +3739,$\beta_Q=(a/Q)\beta_A + (P/Q)\beta_L$ +3740,$r\times n$ +3741,$F(2)=0.75$ +3742,$(80-11)\times 0.25$ +3743,"$S, S^{-1}$" +3744,$\mathsf{Q}'$ +3745,$q(0.1)=1$ +3746,"$k\mathsf E[(X_i-\mathsf E X_i)(X-\mathsf E X)]=k\mathsf{cov}(X_i,X)$" +3747,"$k=0,1,\dots,n-1$" +3748,$q(1-g^{-1}(1-p))$ +3749,$\tilde X_j$ +3750,$\bar F$ +3751,$\pm\infty$ +3752,"$c\in[0,1]$" +3753,$dg$ +3754,$p_Y<0.5$ +3755,$\mathsf E|X|<\infty$ +3756,"$(\mu,\sigma)$" +3757,$\mathsf E[Y\mid \mathcal F']$ +3758,"$(brR15 |- lee.south)+(-0.25,-0.25)$" +3759,$\pi=1.2497$ +3760,$\bar\iota$ +3761,$g(s) \ge 1$ +3762,$v(A\cup B) + v(A\cap B)\ge v(A) + v(B)$ +3763,$\bar P_\tau(a)=\bar P(a) + \tau(a-\bar P_\tau(a))$ +3764,$\nu>0$ +3765,$P_g\{X=M\}=g(0+)>0$ +3766,$\Delta=a'-a$ +3767,$\alpha_i(x)S(x)$ +3768,$\mathbf{\vert S\vert}$ +3769,$\mathsf E[X\mid\mathcal F_0]=\mathsf E[X]$ +3770,$r_h-\mu_L=r-r_L$ +3771,$-0.0012$ +3772,$\rho(X)$ +3773,$\mathsf Q$ +3774,$+1$ +3775,$\mathsf E[X](1+\pi)$ +3776,$\implies\mathsf{FATOU}$ +3777,$\mathsf E[X_0] + \mathsf{VaR}_p(X_1)$ +3778,$1-w$ +3779,$=1/(1-p)$ +3780,$Q_j = 1 - g(S_j)$ +3781,$A(X)$ +3782,$X\ge \mathsf{VaR}_p(X)$ +3783,$\mu(\{0\})=\phi(0)=g'(1)$ +3784,$p_+-p_-$ +3785,"$s\in (0,1]$" +3786,"$p\in (0,1)$" +3787,"$\lambda, \iota, \psi$" +3788,$\Pr(X_{-1}0.95}$ +3927,$g=u^2=0.01$ +3928,$100$ +3929,$X\wedge a \le X$ +3930,"$Y_{t,0}$" +3931,$s>s^\ast$ +3932,$g(s)-\hat g(s)$ +3933,$R:=\bar P_{act}-\bar S$ +3934,$Var[T]=s(1-s)/N$ +3935,$\sum w_i=1$ +3936,$\mathsf E[X] + d(\max(X)-\mathsf E[X])$ +3937,"$\{x_1,...,x_n\mid X < \max(X)-\epsilon\}$" +3938,$z=x$ +3939,$F_n(x)\to F(x)$ +3940,"$\rho(1000, 3000, 3500)$" +3941,$c=2.5$ +3942,$w(x)=e^{kx}$ +3943,$1_\omega(\omega')=1$ +3944,$g(s)=cs$ +3945,$f(t|s)$ +3946,$\displaystyle\int_0^\infty u(x)dF_X(x)$ +3947,$\Lambda\dfrac{\mu_{U}}{\sigma_U} = \dfrac{E( r_{U} ) - r_{f}}{\sigma_{r_{U}}} \left(\dfrac{\mu_{U}}{\sigma_{U}}\right)$ +3948,$f'(x_0)$ +3949,$y^{\ast}-x^{\ast} \ge \epsilon$ +3950,$\mathsf E[X_1]=\mathsf E[Y_{0}]$ +3951,$\mathbf{x_0}$ +3952,$\kappa_i(X)=\mathsf E[X_i\mid X]$ +3953,$g(S(x_{i+1}-))-g(S(x_{i}))$ +3954,$1-g$ +3955,"$d\,F(X)$" +3956,$Q(a)$ +3957,$(1+c)\mu$ +3958,$\mathsf{VaR}_{0.99}$ +3959,$dG(x)=g'(S(x))dF(x)$ +3960,$\rho(c) = c$ +3961,$n=100$ +3962,$\mathsf E[X] + \pi\mathsf{Var}^+(X)$ +3963,$\mathsf E_\mathsf{Q_2}[X_j]$ +3964,$\delta_p$ +3965,$\sigma$ +3966,$\mathsf E[X]=27.5$ +3967,$\mathsf E$ +3968,$\rho(X_0+\epsilon Y)=\mathsf E[(X_0+\epsilon Y)Z_\epsilon ]$ +3969,"$(s(t),m(t))$" +3970,$X>x$ +3971,$\sigma_U = 1$ +3972,"$(p,q(p))=(1-S(x),x)$" +3973,$f(P)=\mathsf E[f(X)]$ +3974,$w_i\ge 0$ +3975,$\int X_n\to 0$ +3976,"$r_f\ge 0, r>0$" +3977,$Z$ +3978,"$X_1,X_2$" +3979,$r_L$ +3980,"$\Omega=[0,1]\times [0,1]$" +3981,$x_i$ +3982,$P_i \ge \mathsf E[X_i]$ +3983,$a(X)$ +3984,$g(s)+g'(s)(1-s)\ge 1$ +3985,$\mathbf{\kappa_1}$ +3986,"$\mathsf{cov}(X_i,\sum_j X_j)=\mathsf{cov}(X_i,X_i)=\mathsf{Var}(X_i)>0$" +3987,$\mathsf E[X1_A] / \mathsf E[1_A]$ +3988,$\mathsf Q(A)=0$ +3989,$0-\rho(-H)$ +4010,"$Y_{0,1}$" +4011,$a(X;X)=\rho(X)=\sum_i a_i$ +4012,$\displaystyle\int_0^\infty xg'(S(x))f(x)dx$ +4013,$A(X)\not= B(X)$ +4014,$\lim_{y\uparrow x} f(y)$ +4015,$\displaystyle\int_\Omega X(\omega)\Pr^*(d\omega)$ +4016,$\psi^{-1}(p)$ +4017,$\mathcal Q\subset\mathcal M(\mathsf P)$ +4018,"$a(x_1,\dots,x_n):=a(X(x_1,\dots,x_n))$" +4019,$1-q$ +4020,$ds(t)/dt$ +4021,$X_{-3}=C'_1 + \cdots + C'_n$ +4022,$g(S(M-))/S(M-)$ +4023,$\mathsf{VaR}_{p_0}(X)=\sup X$ +4024,$p=1/2$ +4025,$y\not\in C$ +4026,$S=\Pr\{X>x\}$ +4027,$X_0=C_1 + \cdots + C_N$ +4028,$\mathsf E[g'(S(X))]=1$ +4029,"$2^0, 2^2, 2^4, ...$" +4030,$F_I$ +4031,$gdX$ +4032,$b_l \le 1 \le b_h=2-b_l$ +4033,$30+10t$ +4034,$m_1$ +4035,"$Y_{t,d}$" +4036,$F(x)=\sup\{ p\mid q(p) < x \}$ +4037,$\mathsf E[X \mid X \ge x] = \mathsf E[X 1_{X \ge x}] / \Pr(X \ge x)$ +4038,"$X_{i,j} \leftarrow \kappa_{i}(X_j)$" +4039,$1/g'(0)$ +4040,$1-g(1-p)$ +4041,$d\Pi = (r_h-\mu_L)\Pi dt$ +4042,$q(U_X) = m$ +4043,$\alpha_i(t)$ +4044,$U=X+Y$ +4045,$p^\ast$ +4046,"$\mathbf{D^f\rho_{X\wedge 30,X}(X_2)}$" +4047,"$0,0,0,1,2,5,8,12,23,40$" +4048,$0\le k < 2^m$ +4049,"$c=1,2,3$" +4050,$E[s]=0.1160$ +4051,$\mathbf{X\wedge a}$ +4052,"$\lambda([a,b]) = b-a$" +4053,$p^+$ +4054,$\mathsf E X + c{X-\tau }_p$ +4055,$S_X(t)=S_{X\wedge a}(t)$ +4056,$\mathsf E[\log(X)]$ +4057,$h(X)=X$ +4058,$D_1\supset D_2\supset \cdots \supset D_\infty$ +4059,$g''(s)=-\phi'(1-s)\le 0$ +4060,$\prec_1^*$ +4061,$X=100$ +4062,$X\wedge a(X)$ +4063,$\mathbf{X}$ +4064,$\times$ +4065,$\bar M(a)$ +4066,$\mathsf{LI}$ +4067,$(p_0 < p^\ast < p_1)$ +4068,"$c = 0.5,1.0,\dots,2.5$" +4069,$\sup X_n=1\not=\sup X=0$ +4070,$IL$ +4071,$\mathsf E[WX] \le \rho(X)$ +4072,$S(x)\leftrightarrow g(S(x))$ +4073,$\Pr(X=\mathsf{VaR}_p(X))=0$ +4074,$\lambda=\sum_i \lambda_i$ +4075,$\mathsf{TVaR}_{0.8}$ +4076,$Q = M/\iota$ +4077,$(a_i)_i$ +4078,$g(s)=d+sv$ +4079,$p\nu_p$ +4080,$\mathsf{TVaR}_p(X)=\mathsf E[X\mid X >\mathsf{VaR}_p(X)]=\sum_i\mathsf E[X_i\mid X>\mathsf{VaR}_p(X)]$ +4081,$f_i$ +4082,"$X_{0,2}$" +4083,$aq_X(p) \}$ +4108,$S(x)>>0$ +4109,$q_B \le q_C$ +4110,$\mathsf{TVaR}_{0.75}$ +4111,$g'(s) < \infty$ +4112,$\hat p$ +4113,$\kappa_i(q(1-g^{-1}(1-\tilde p)))$ +4114,$q^-(p)$ +4115,$\rho(X-\rho(X))=\rho(X)-\rho(X)=0$ +4116,$g_0$ +4117,$dt\to 0$ +4118,$\{X\in L^\infty \mid \rho(X)\le c \}$ +4119,"$Y_{2,2}$" +4120,$\mathsf P(f^{-1}(A))=\Pr(A)$ +4121,"$c_i=\displaystyle\int_0^1\dfrac{\partial c}{\partial x_i}(tx)\,dt$" +4122,$\rho(X_{-1}\wedge a_{ro})={{mvp_ro}}$ +4123,$\bar \iota = \dfrac{\bar M(a)}{\bar Q(a)}$ +4124,$\mathcal{N}_{X\wedge a}(X_i(a))$ +4125,$f'>0$ +4126,"$\bar M_{t,0}$" +4127,$E$ +4128,$p^\ast = 0.48732$ +4129,$r_P$ +4130,$S=g(S)=1$ +4131,$\mu_d = (6-d)^2$ +4132,$g(s)=0.9s + 0.1$ +4133,$\left( g(S(x_{(j)}))-g(S(x_{(j-1)})) \right) / ( x_{(j)}-x_{(j-1)} )$ +4134,$t^\star$ +4135,$1_Z$ +4136,$\Pr(E')=1-\Pr(E)$ +4137,$\omega < p^-$ +4138,$\rho_g(X)=\mathsf E[X]$ +4139,$q = s$ +4140,$a_i=\mathsf E_\mathsf{Q}[X_i]$ +4141,"$s\in (0,1)$" +4142,"$\omega\in [0,0.1)\cup [0.25, 0.35) \cup [0.5, 0.6) \cup [0.75, 0.85)$" +4143,$80-11=69$ +4144,$g'$ +4145,$\rho(X)+c$ +4146,$S(x)=(1+x)^{-\alpha}$ +4147,$r_M$ +4148,$U(2)=0$ +4149,$\alpha_i(x)$ +4150,$\sup X\le \sup Y$ +4151,$\mathsf E[X_1\mid X < 2^{-m}]$ +4152,$S(x)=\Phi((-x+\mu)/\sigma)$ +4153,$\tilde X_1 + \tilde X_2 \succeq^2 \tilde X_1$ +4154,$p=F(a)=1-S(a)$ +4155,$v\mathrm{EL}+da\ge \mathrm{EL}$ +4156,$X=X_s + X_c$ +4157,"$\mathsf{VaR}_{0.995}=64,861$" +4158,$\mathbf{X_{2}}$ +4159,$P = 3.1035$ +4160,$x=q(1-g^{-1}(1-p)))$ +4161,"$d=1,2,\dots$" +4162,$h=1$ +4163,"$k_1, k_2$" +4164,$p=0.95$ +4165,"$s^{\ast}=1/2, \lambda^{\ast}=0$" +4166,$\esssup(X)=1$ +4167,$1-p \ge g^{-1}(1-p) \implies 1-g^{-1}(1-p) \ge p \implies q(1-g^{-1}(1-p))>q(p)$ +4168,$\Pr(X_n\in A)=1$ +4169,"$x+y\wedge aX =\min(x+y,aX)$" +4170,$\mathsf{Q}(A)=\mathsf E_\mathsf{Q}[1_A]$ +4171,$H(X)x]=x+\mathsf E[X]$ +4178,$\mathbf{n}$ +4179,$\mu = t \nu$ +4180,$(1)(0.25)+(90)(0.25)=22.75$ +4181,$W = 0$ +4182,$\rho(X)=51.3887$ +4183,"$\{1,2 \}$" +4184,$\mathsf E[X] +\lambda\mathsf E[(X-\mathsf E X)^+]$ +4185,$d=i/(1+i)$ +4186,$\beta_2$ +4187,$Q=\nu a'$ +4188,$\{ X >q(p) \}$ +4189,"$g'>0, g''<0$" +4190,$Y=c\in \mathbb R$ +4191,$h(u)=1$ +4192,$\bar P_d=\mathsf E[Y_{d}]+\lambda\sigma(Y_{d})$ +4193,$\lim_{\epsilon \downarrow 0} (f(x+\epsilon)-f(x))/\epsilon$ +4194,$\omega_1$ +4195,$r>0$ +4196,"$\alpha_i(\mathbf{v}, x)$" +4197,$\omega\ge 0.4$ +4198,$\mathsf E_{\mathsf Q}[X_i]=\mathsf E[X_ig'(S(X))]$ +4199,$L(X)=(X-\mathsf E X)/\mathsf{SD}(X)$ +4200,$\bar q_{X_1+X_2}(s) \le 2\bar q(s)$ +4201,$f(t)=\rho(tX)$ +4202,$X_n\uparrow 1$ +4203,$\int S(x)dx$ +4204,$A\subset \Omega$ +4205,$\mathsf E[(X-x_l)^+]$ +4206,$(A-L)^+$ +4207,$P(x)/Q(x)$ +4208,$1+Z-\mathsf E Z$ +4209,"$\bar Q_{0,0}$" +4210,$r_U \Delta A - \Delta P$ +4211,$s_0=0$ +4212,$\mathsf E[(X-\mathsf E X)^+]={(X-\mathsf E X)^+}_1$ +4213,$g(S_{\mathsf{j}(a)})=0.5$ +4214,$-g''(s)=\alpha(\alpha-1)s^{\alpha-2}$ +4215,$\mathsf E[g'(S(X))]=\int_0^\infty g'(S(x))dF(x)=\int_0^\infty -\frac{d}{dx}g(S(x))dx=g(S(0))-g(S(\infty))=g(1)-g(0)=1$ +4216,$\bar Q(a) =a-\bar P_g(a)$ +4217,$\exp(a)$ +4218,$s\mapsto g(s)$ +4219,$\alpha X$ +4220,$c(S)\le c(T)$ +4221,$(1-\lambda)(1+\gamma)$ +4222,$1-\beta_i(t)g(S(t))$ +4223,$\mathsf E[X_ih(X)]=\mathsf E[\kappa_i(X)h(X)]$ +4224,$L_a^{a+da}$ +4225,"$a_{0,t}' := a_{0,t-1}-X_{0,t}$" +4226,$-Y$ +4227,$W_{t}$ +4228,$2^n$ +4229,$(1 - \nu F(a))$ +4230,$<$ +4231,$x=\sum_i \mathsf E[X_i\mid X=x]$ +4232,$g'\left (S_X(X)\right )$ +4233,"$X_1=(0,0,0,0,0,0,2,4,8,0)$" +4234,$R_L=R_f + \beta_L(R_M-R_f)$ +4235,$cv=0.137$ +4236,"$(2,2)$" +4237,$1/x$ +4238,$A(1_{X_1>x_1}+1_{X_2>x_2}) \le A(1_{X_1>x_1}) + A(1_{X_2>x_2})$ +4239,$\Delta=\Phi(d^*)$ +4240,$\alpha(\mathbb{Q})$ +4241,$F_g(x) = 1- g(S_X(x))$ +4242,$Z(1000)=(1-0)/(0.1-0)=10$ +4243,$\bar S(a)=\mathsf E[X\wedge a]$ +4244,$\tau=1$ +4245,$\rho(X_1) \ge D\rho_X(X_1)$ +4246,"$\mathcal Q =\{ \mathsf Q \mid \mathsf Q\ll \mathsf P,\ \alpha(\mathsf Q)=0 \}$" +4247,$\Pr(X < x)\ge 1/6$ +4248,"$X_j=\sum_i X_{i,j}$" +4249,$\mathsf{SD}$ +4250,$n>1$ +4251,$-\phi(d^*)<0$ +4252,$\rho(\tilde X+X)=\rho(\tilde X)+\rho(X)$ +4253,$a(\mathbf{v})$ +4254,$P(dx)$ +4255,$\mathsf Q(X>a)/P_X(X>a)=g(S(a))/S(a)$ +4256,$\rho(X-P)=\rho(X)-P$ +4257,$a+da$ +4258,$r_pq$ +4259,"$m\ge 1, n\ge 0$" +4260,$(1-g)$ +4261,$x=2$ +4262,$T_k$ +4263,$X\le c$ +4264,$t$ +4265,$X \succeq Y$ +4266,$\mathsf E_{\mathsf Q}[Y]$ +4267,$x=a$ +4268,"$\mathsf{biTVaR}_{p_0,p_1}^w(X)=\bar P$" +4269,$\log(X)$ +4270,$\nu^{-1}\mathsf E[\nu(X)]$ +4271,"$[0, 1-p)$" +4272,$\mathsf{VaR}_{0.95}(X)$ +4273,$S_t=a_0 + (1+c)\mu t - X_t$ +4274,$1/(1+r) = 0.893$ +4275,$D^n\rho_X(X_i)$ +4276,$A\subset \mathbb{R}$ +4277,$\bar P_t = \rho(Y_{t})$ +4278,$W_1$ +4279,$s/(1-s)$ +4280,$E_1$ +4281,"$f:[0,1]\to[0,1]$" +4282,$A\cap B$ +4283,"$(p,q(1-g^{-1}(1-p)))=(1-g(S(x)),x)$" +4284,$X_1=0$ +4285,"$\beta = \mathsf{cov}[r,r_M]/ \sigma^2_{r_M}$" +4286,"$f(x, \cdot)\in L_p(\Omega, \mathcal{F}, \mathcal{P})$" +4287,$\bar P(a)=\rho_g(L_0^a(X))$ +4288,$S_t=\exp(\mu t + \sigma W_t)$ +4289,$P_i(x)=\beta_i(x)g(S(x))$ +4290,$1-L/P = (P-L)/P$ +4291,"$x_{1,2}$" +4292,$w/(1-w)$ +4293,$\sup_\Omega |X_n - X| \to 0$ +4294,$\mathsf E_{\mathsf{Q}}[X\wedge a] \le \rho(X\wedge a)$ +4295,$\beta_i(a) g(S(a))$ +4296,$\mathsf E[Y]$ +4297,$\prec_n^*$ +4298,$2^{-t}$ +4299,$X_2/X$ +4300,$\Delta X=80-11=69$ +4301,$g(S(x))=\exp(-\alpha H(x))$ +4302,$\mathsf E[X_i \mid X=x]$ +4303,$\rho(\lambda X + (1-\lambda)\rho(X))$ +4304,$X\le Y+\Vert X-Y\Vert$ +4305,$(1-p)/(p\nu(p)^2)$ +4306,$I(F(x) < p)=\begin{cases} 1 & F(x)< p \\ 0 & F(x)\ge p\end{cases}$ +4307,$\mathsf E[U]=\mathsf E[X]$ +4308,$g(s)=1$ +4309,$x < x^\ast$ +4310,$\mathsf E[X] + c\mathsf E[(X-\mathsf E X)_+^2]$ +4311,$X\wedge a(X)\le Y\wedge a(Y)$ +4312,$t\uparrow 0$ +4313,"$\eta_{p,\alpha_1}(X) < \eta_{p,\alpha_2}(X)$" +4314,$\phi(t)=\int_0^t (1-p)^{-1}\mu(dp)$ +4315,$a_{\min}$ +4316,$\mathbf{t+1}$ +4317,$x\ge a$ +4318,$N=r_a$ +4319,$\int S(x)dx = \int xdF(x)$ +4320,$\mathsf{VaR}_{0.7}(X)=$ +4321,$\mathsf P(X=\sup(X))>0$ +4322,$\bar M_i(a) = \bar P_i(a) - \mathsf E[X_i(a)]$ +4323,$L(X)=(1-p)^{-1}1_{X\ge x_p}(X)$ +4324,$\mathsf E[X_i]$ +4325,$\mu = w \delta_{\alpha_1} + (1-w) \delta_{\alpha_2}$ +4326,$\mathsf{TVaR}_{0.95}(X)=\mathsf E[XZ]$ +4327,$A(-X)$ +4328,$\mathsf{j}(90)=6$ +4329,$a - P$ +4330,$q^-_X(0.95)$ +4331,$1100 \le x \le 1250$ +4332,$\sigma\sqrt{t}$ +4333,$(L-A)^+$ +4334,"$\int Zd\mathsf P = \int d\mathsf Q/d\mathsf P\, d\mathsf P = \int d\mathsf Q =1$" +4335,$\mathcal A$ +4336,$d\mathsf Q/d\mathsf P$ +4337,$\mathbf{X_{n}}$ +4338,$t_f$ +4339,$\hat q(p)$ +4340,$p<1$ +4341,$r < n$ +4342,$\mathcal S(X)=\mathsf{VaR}_p(X)$ +4343,"$(\omega',\omega'')$" +4344,$\mathbf{X_{2}(a)}$ +4345,"$u\in[0, 1-p]$" +4346,$k_i=a_i/v_i$ +4347,"$(s_j, g_j)$" +4348,"$(3,3)$" +4349,$T(p)$ +4350,$D/C$ +4351,"$s\in[0, 1-p]$" +4352,$p=1$ +4353,$a_{d}' = a_{d-1}-X_{d}$ +4354,$g'\left (S(X)\right )$ +4355,$p=0.75$ +4356,$\{\omega\mid X(\omega) = x_1\}$ +4357,$\tau a_i$ +4358,$d\downarrow 0$ +4359,$p\ge 1$ +4360,"$g(s)=\min(s/(1-p),1)$" +4361,$\phi'(p)\ge 0$ +4362,$\mathit{ROE}(s) = r_f + Ck(s)$ +4363,$q(p)\phi(p)$ +4364,$\mu_0=\mu_1$ +4365,$w_l=1-c\gamma$ +4366,$0.7 \le p < 0.8$ +4367,"$j=1,\dots, n$" +4368,$x=q_X(1-s)=\mathsf{VaR}_{1-s}(X)$ +4369,$\{p \ge p_-\}$ +4370,$(1-p)^{-1}$ +4371,$\rho(X)=\rho(\mathsf E[X]+X-\mathsf E[X])=\mathsf E[X] + \rho(X-\mathsf E[X])$ +4372,$\omega<1/n$ +4373,$\mathsf E[X_i\wedge a_i]$ +4374,$\tilde X = (x_{ij})$ +4375,$q(p)=c$ +4376,$a(X_i;X)\le \rho(X_i)$ +4377,$\rho(0) \ge 0$ +4378,$g'(s-)\ge 0$ +4379,$\exists$ +4380,$^1$ +4381,$x^{-\alpha}$ +4382,$k>1$ +4383,$D\rho_X(X_2)=45.1801$ +4384,$\mathsf E[X^2]$ +4385,$\mathsf E[|X|]<\infty$ +4386,$V(2)$ +4387,"$\rho_g(X)=\int_0^\infty g(S(x))\,dx$" +4388,$c(1)$ +4389,$X=X_{-1}+X_{0}$ +4390,$xf(x)dx$ +4391,$t=0.06405$ +4392,$Y_{0}=\sum_{d>0} X_{d}$ +4393,$a=Q+P$ +4394,$Y\preceq Z$ +4395,"$a_{0,0}:=a(Y_{0,0})$" +4396,$X_1+X_2\sim 2X$ +4397,$l$ +4398,$\WCE_p(X) := \sup\ \{ \mathsf E[X \mid A] \mid \Pr(A) > 1-p \}$ +4399,$r_h=r+\pi$ +4400,$\Delta Q_{ro}(a)$ +4401,$\bar Q_{0}$ +4402,$=1-\nu F(a)$ +4403,$X \le 0$ +4404,$\mathsf E[X_2(a)\mid X_1(a)=x] \le a-x$ +4405,$X^{-1}(A)\in\mathcal F$ +4406,$\sup(X\wedge a)=a$ +4407,$\mathbf{P_i} \in \mathbb{R}^2$ +4408,$\bar\nu=1/(1+\bar\iota)$ +4409,$\rho(X/n)=\rho(n(X/n))/n=\rho(X)/n$ +4410,$\mathsf x\mathsf{TVaR}$ +4411,$1_{U_X\ge p}=0$ +4412,$F(X) - F_X(X-)=0$ +4413,$\tilde X$ +4414,$m'(0) = (m_1-m_0)/s_1$ +4415,$B \in\mathcal B_p$ +4416,$1/16$ +4417,$\bar\iota(a)=\bar\iota$ +4418,$\mathsf E X + \inf_x \{\alpha_1\mathsf E[(x-X)^+] + \alpha_2\mathsf E[(X-x)^+] \}$ +4419,$\mathsf P(X=X(\omega_0))>0$ +4420,$X=X_i + (X-X_i)$ +4421,$\rho(X_1+X_2) \le \rho(X_1)+\rho(X_2)$ +4422,$(0)$ +4423,$\mu_i$ +4424,$\mathsf{VaR}_1=\esssup$ +4425,$\mathsf E[X_i/X\mid X>x]$ +4426,$#4$ +4427,$v=x$ +4428,$\phi(p)=g'(1-p)\ge 0$ +4429,"$(0,0)$" +4430,$s_2$ +4431,$F(x) < p \iff q^-(p) > x$ +4432,"$g(S)\,\Delta X$" +4433,$\delta+\nu$ +4434,$E'$ +4435,$\mathsf P(X\ge x_p)=1-p$ +4436,$\mu=7.8044$ +4437,$\rho(X)=\mathsf E[X] + c\mathsf{Var}(X)$ +4438,$a_{2}'$ +4439,$\Pr(X<2)=1/6<\Pr(X\le 2)=1/3$ +4440,$p>0$ +4441,$z$ +4442,$\mathsf{j}(91)=7$ +4443,$\zeta_s = 8$ +4444,$ag(0+)$ +4445,$\rho-\iota g>0$ +4446,$R = P-L$ +4447,$\mathrm{sgn}(z)|z|^{1/(q-1)}/\|z\|_p^{q/p}$ +4448,$o(dt)$ +4449,$q^-$ +4450,$A_4 = [0; \epsilon_1 + \epsilon_2]$ +4451,$\mathsf{Var}(Y) \ge \mathsf{Var}(X)$ +4452,$\esssup(X)=\sup\{x\mid \Pr(X>x)>0 \}$ +4453,$0\le \omega\le 1$ +4454,$q(p)=e^{\mu+z_p\sigma}$ +4455,$\mathsf E_\mu[\phi(\mathsf E_\pi u\circ f)]$ +4456,"$[f'_-(x_0), f'_+(x_0)]$" +4457,$a(\cdot)$ +4458,$\mathsf E[(a-X)^+]$ +4459,$L_p$ +4460,"$X\ge 0,(\tilde X-X)\ge 0$" +4461,$\rho(\lambda X)$ +4462,$\mathsf E[Z]\le 1$ +4463,$Pr(X_{-1} > a)$ +4464,$X\wedge a / X$ +4465,$\pi^{-1}\log\mathsf E[e^{\pi x}]$ +4466,$\tau=-1$ +4467,$\mathsf{TVaR}_{p^*}$ +4468,$Z>\mathsf E Z$ +4469,$X\ge x_p$ +4470,$\mathsf E[Y\mid \mathcal F']=\mathsf E[Y\mid X]=\mathsf E[X+Z\mid X]=X +\mathsf E[Z\mid X]=X$ +4471,$\mathbf{X_{2}/X}$ +4472,$A(1_{U>0.95})=A(1_{U\le 0.05})=g(0.05)=0.3017$ +4473,$\mathsf{TVaR}_{0.9}$ +4474,$2.576\sigma_d$ +4475,$\mathsf{TVaR}_1$ +4476,$\Pr(X_n=0)=1-1/n$ +4477,$D/L=\mathsf E[A\wedge L]/\mathsf E[L]$ +4478,$\bar P_n$ +4479,$F_0 = P_{act}-\mathsf E_{rn}[U]$ +4480,$\mathit{MV}_{gc}(a_{gc})=a_{gc}-\rho(X\wedge a_{gc})={{mv_gc}}$ +4481,$1\wedge \cdot$ +4482,"$g(s)= \displaystyle\int_0^s \phi(1-p)dp = \min(s/(1-\alpha), 1)$" +4483,$\ll$ +4484,$0\le \alpha \le 1$ +4485,$Z\succeq_2 \mathsf E[Z\mid X]$ +4486,$j=8$ +4487,$S_0=1-p_0$ +4488,$g_{ROC}$ +4489,$\rho_1(X)$ +4490,$f(s) \ge s$ +4491,$Q(a)=h(F(a))$ +4492,$\mathsf E[X_i g'(S(X))]$ +4493,"$\bar P_i(v_1, v_2, a) / v_i$" +4494,$q_C\le q_A$ +4495,$. Thus $ +4496,$k\mapsto k\rho(-X)$ +4497,$\mathsf{TVaR}_1=\sup$ +4498,$\lambda = \dfrac{E( r_{M} ) - r_{f}}{\sigma_{rM}}$ +4499,$g'(1)<1$ +4500,$u'''' \le 0$ +4501,$-X_i$ +4502,$ROE=(g-s)/(1-g)=m/(1-s-m)$ +4503,$X > a$ +4504,"$f(0,0)=0$" +4505,$\mathsf{Var}$ +4506,$l(kX)\le\rho(kX)$ +4507,$\lambda \ge 0$ +4508,"$0, 1/p$" +4509,$X\ge m$ +4510,$E(X_{0}(a))$ +4511,"$(0,1)$" +4512,$i=1\dots N$ +4513,$-(1-s)g''(1-s) + g(0+)\delta_1 + \sum_s s\Delta_s \delta_{1-s} + g'(1)\delta_0$ +4514,$\phi(0)=\mu(\{0\})$ +4515,$X_1=X_2=10$ +4516,$\mathbf{Z_5}$ +4517,$80=9.56 + 70.44$ +4518,"$\kappa_{i}(x) = \dfrac{\sum_{j:X_{j} = x} X_{i,j} p_j}{\sum_{j:X_{j} = x}p_j}$" +4519,$S(p)=1-p$ +4520,$x=q(\hat p)$ +4521,$g(s)\le 1$ +4522,$N\times d$ +4523,$X=a$ +4524,$P_{g}$ +4525,$x=q_{\mathbf{v}}(s)$ +4526,$dW_t$ +4527,$a_x=2$ +4528,$f(x)=\exp(-x/\mu)/\mu$ +4529,$\bar M_i(a)$ +4530,$Z\in \mathcal Q$ +4531,$U=4$ +4532,$f(x)=e^x$ +4533,$X_{-1}=C_1 + \cdots + C_N$ +4534,$M_i(x)+Q_i(x)$ +4535,$\pi-\lambda\mathsf E[X]$ +4536,$\mathbf{\sigma}$ +4537,$V=1_{X\le x^\ast}$ +4538,$\mathsf E[X(1_{U_X\ge p}-B)]=\mathsf E[(X-m)(1_{U_X\ge p}-B)]\ge 0$ +4539,$\bar Q_{2}$ +4540,$\bar P_g(a)=\rho(X\wedge a)$ +4541,$g''(s)=0$ +4542,$K=3$ +4543,$g(s)=\sqrt s$ +4544,"$\bar P_{0,0}$" +4545,"$(x,-x)$" +4546,$n=9$ +4547,$\hat q(p)=q(1-g^{-1}(1-p))$ +4548,$A(0)=0$ +4549,$\mathsf E_\mathsf{Q}[X_i] = \mathsf E_\mathsf{Q}[\mathsf E_\mathsf{Q}[X_i \mid X]]$ +4550,$\rho(X)\le\liminf \rho(X_n)$ +4551,$w(Z)/\mathsf E[w(Z)]$ +4552,$\mathsf E[YZ]\le 0$ +4553,$c$ +4554,$p^*=48.25/71=0.6796$ +4555,$d\tilde p=g'(1-p)dp=\phi(p)dp$ +4556,$BC$ +4557,$1 in a layer with loss probability $ +4558,"$a_i=\mathsf E[X_i] + k\mathsf{cov}(X_i, X)$" +4559,$d=1$ +4560,$s/g(s)\le 1$ +4561,$\mathsf E[X_i\tilde Z]=\rho_g(X)/2$ +4562,$1/\lambda$ +4563,$1-\alpha_i(x)S(x)$ +4564,$Z=Z_X$ +4565,"$(-\mathsf x*0.75, -2)$" +4566,$E[Z]$ +4567,$\sum_i X_i(a)=X\wedge a$ +4568,$\mathsf{P}(\{X\in A\})$ +4569,$M(x)/Q(x)$ +4570,"$(\Omega, \mathcal F, \Pr)$" +4571,$d\omega$ +4572,$\mathsf E[(X_i/X)g'(S(x)) \mid X > x]$ +4573,$\mathcal{Q}$ +4574,"$(x_B, g(S(x_B-))$" +4575,$X=q(U)$ +4576,$q_A(p) = \sup A$ +4577,$\lambda > 1$ +4578,$a \in \mathbb{A}$ +4579,$y\le q_C(p)$ +4580,$\mathsf{TVaR}_{0.95}(Y)=0.8\mathsf E[X]=2000$ +4581,$\rho(kX)$ +4582,$u=ug(1)=ug(1)+(1-u)g(0) \le g(u)$ +4583,$\Delta Q_{ro}(a) = a-a_{ro}$ +4584,$x_A=\partial x/\partial A$ +4585,$\mathsf{TVaR}_0$ +4586,$\lambda=0.73$ +4587,$Q^* > S$ +4588,$c\le 1$ +4589,$\omega=1$ +4590,$p<0.9$ +4591,$\tau=0.03$ +4592,$\Pr(A)=1-p$ +4593,"$\beta, \kappa$" +4594,$a=a_0+(1+c)\mu$ +4595,$f_{\mathbf{v}}$ +4596,$\mathsf E[X]+kR(X)$ +4597,$\frac{1}{1-p}\int_{1-p}^q \mathsf{VaR}_s(X)ds$ +4598,"$\bar L, \bar P, \bar M$" +4599,"$(\mathsf x*.75, -2)$" +4600,$\mathsf E[W]$ +4601,$\nu$ +4602,$\tau$ +4603,$x_l < x=\mathsf{VaR}$ +4604,$0\le p < 1$ +4605,$Z\mid X$ +4606,"$X:\Omega\to[0,\infty)\subset \mathbb R$" +4607,$\Pr(X < x) \le 0.4 \le \Pr(X\le x)$ +4608,"$[a, a+da]$" +4609,$f>0$ +4610,$S(x-)=0.1$ +4611,$\rho(X)\le b$ +4612,$\mathsf E[X_i/X|X>a]$ +4613,$s=0.45$ +4614,$(1-p)$ +4615,$Z(X(\omega))$ +4616,$\mathit{MV}_{ro}(a) = a-P(X_{-1}\wedge a)$ +4617,$\mathsf E[X^k]\le \mathsf E[Y^k]$ +4618,$9+1=10+0=10$ +4619,$g \circ S$ +4620,$\Pr(X=x_i)=\Pr(X>x_{i-1})-\Pr(X>x_i)=S(x_{i-1})-S(x_i)$ +4621,$r_f>0$ +4622,$X\wedge a$ +4623,$\mathsf E[(X-a)^+]/\mathsf E X$ +4624,$NT$ +4625,$p/\mathsf E[p]=p(1+r_f)$ +4626,$p\ge p_0$ +4627,$-\rho(-H)=\rho(H)$ +4628,$\mathcal Q(X)=\{ \mathsf Q\in\mathcal Q\mid \rho(X)=\mathsf E_\mathsf{Q}[X] \}$ +4629,$L_X(X)=\rho(X)$ +4630,"$\{(s_j, g_j)\} \cup \{(0,0), (1,1)\}$" +4631,$\displaystyle\int_0^\infty xdF(x)$ +4632,$g = s^{0.4}$ +4633,$\mathsf E_{\mathsf Q}[Y] = \mathsf E[YZ]$ +4634,"$0.06 \times (64,861 - 7,500)=3,442$" +4635,$a_1'=a_0-X_{1}$ +4636,$N(t)$ +4637,$v=S$ +4638,$\mathsf{VaR}_p(X)$ +4639,$u^{iv}<0$ +4640,$\lambda_1$ +4641,$X_1=c_1-Y/2$ +4642,$\alpha < 1$ +4643,$Y+W$ +4644,$\mathsf E[Z_A\mid X]$ +4645,$\bar q(s)=q(1-s)$ +4646,$L-f(L)$ +4647,$X=MX_2$ +4648,$a=a(X)$ +4649,$\alpha_i(a)$ +4650,$\bar\iota : 1$ +4651,$a < kP$ +4652,$X_i/X$ +4653,$\partial a/\partial v_i$ +4654,$U(-X)\ge U(-Y)$ +4655,$\rho(X)\le \lim\rho(X_n)$ +4656,$wq_Y(p)+(1-w)q_Z(p)$ +4657,$\Pr(X>\mathsf{VaR}_p(X))>1-p$ +4658,$p^-$ +4659,$h(0)=0$ +4660,$0\le p^\ast\le 1$ +4661,$\alpha\ge A(n)=\sum_s n_s(1-g(s))$ +4662,$af=1$ +4663,$N=n$ +4664,$q=1-p$ +4665,"$\{x_1,\dots,x_N\}$" +4666,$\Pr(\{\omega_2\})=2/3$ +4667,"$(0,0,0,0,0,0,0,0,5,5)$" +4668,$X_n(\omega)=0$ +4669,$\kappa_1(10) = \mathsf E[X_1\mid X=10]$ +4670,$1-s_j$ +4671,$\mathsf{TVaR}_p(X)-\mathsf{VaR}_p(X)=\sigma(\phi(\Phi^{-1}(p))/(1-p) - \Phi^{-1}(p))\to 1$ +4672,$\alpha_j'(x)<0$ +4673,$P=D$ +4674,$f(w) = \exp(-w)$ +4675,$1+r^*=(1+r)(1+\tau)$ +4676,$a=P+Q$ +4677,$X\wedge 10$ +4678,"$u\in[0,1]$" +4679,$L_0^l(X)$ +4680,$j=1$ +4681,$\mathbf{X_{1}/X}$ +4682,$g(s)=\mathsf{TVaR}_{.99}$ +4683,$m+1$ +4684,$\mathsf E[X_1\mid X_1+X_2=x]=mx/(m+n)$ +4685,$\mathsf E[X\wedge a]$ +4686,$9.67$ +4687,$L^*$ +4688,$\|\cdot \|_\rho=\rho(|\cdot |)$ +4689,"$(x_{2,1}, x_{2,2})$" +4690,"$(x,y)$" +4691,$p>1$ +4692,$\mathcal S(X)=\mathsf E[X]$ +4693,$\mathbf{X_{1}(a)}$ +4694,$\rho(X)=\mathsf E_\mathsf{Q}[X]-\alpha(\mathsf Q)$ +4695,$1-2c\Pr(Z>\mathsf E Z)$ +4696,$\mathsf{VaR}_1$ +4697,$p=\Phi^{-1}(4)=3.17\times 10^{-5}$ +4698,$g(s)=s^a$ +4699,$X_i\Delta g(S)$ +4700,$x'$ +4701,$\rho_g(X)=51.156$ +4702,$\rho(X)= \mathsf E_{\mathsf{Q}_X}[X]$ +4703,"$(s,g(s))=(0.2, 0.36)$" +4704,$\delta^{\star}$ +4705,$\mathsf Q^t\cdot X$ +4706,$0=\Pr(X<1)<1/6=\Pr(X\le 1)$ +4707,$s(0)=s_0=0$ +4708,$dS=-f(x)dx$ +4709,$1_{\{X>x\}}$ +4710,$\ge x$ +4711,$g'(1-p)$ +4712,$\mathbf{s_3}$ +4713,$Z(x)$ +4714,$0.495(r-i)$ +4715,$\tau(a-\bar P_\tau(a))$ +4716,$\mathsf E[X_2\mid X=x]$ +4717,"$\bar Q_{0,2}$" +4718,"$u'>0, u''>0$" +4719,$Y(\omega)=0$ +4720,$g(S(x))=s$ +4721,$P/S$ +4722,"$p\in[0,1]$" +4723,$X=F^{-1}(U)$ +4724,$>1$ +4725,$r\times m$ +4726,$P = \mathsf E[X] + \pi\mathsf{Var}^+(X)$ +4727,$s=0$ +4728,$\hat q(p)=x$ +4729,$\mathscr{O}(f)$ +4730,"$1/2,1/4,1/4$" +4731,$n-5$ +4732,$q(1-g^{-1}(1-p))/q(p)$ +4733,$Z-X$ +4734,$\mathbb{Q}'$ +4735,$s>0$ +4736,"$\pmb{j, p, S, \kappa_1, \Delta X, \Delta(X\wedge a)}$" +4737,$S(x)$ +4738,$0\le x < 1/6$ +4739,"$\mathbf{g(S)\,\Delta X'}$" +4740,"$\omega=0,1,\dots, 99$" +4741,$\tilde Z_X:=\mathsf E[Z\mid X]$ +4742,"$0,0,1,2,3,6,10,18,36,52$" +4743,$t=0$ +4744,$p=0.791$ +4745,$f(x+)$ +4746,$X_{2c}$ +4747,$\mathcal S$ +4748,$\mathsf E[u(w-X)] = u(w-c)$ +4749,$0\le \Pr(E)\le 1$ +4750,$q_{\mathbf{v}}(p)=\mathsf{VaR}_p(X(\mathbf{v}))$ +4751,$p(\omega)$ +4752,$\rho(X)=\mathsf E[Xe^{kX}]/\mathsf E[e^{kX}]$ +4753,$0\le p^*\le 1$ +4754,$r_N$ +4755,$\rho(X_g)-\rho(X_n)=51.1560-49.8986=1.2574$ +4756,$S(x)=0$ +4757,$5/6$ +4758,$s^\ast=1/2$ +4759,"$a_{0,t}:=a(Y_{0,t})$" +4760,$0\le p_0 \le p_1\le 1$ +4761,$0.2$ +4762,"$X_1,X$" +4763,$(1-r_0)\delta_1$ +4764,$\mathsf E[X_i \mid X]$ +4765,"$[0,1-p)$" +4766,$\mathsf E[Z]=g(1)-g(0)=1$ +4767,$\mathcal Q_2$ +4768,$\lambda\rho(X)$ +4769,$\rho\mapsto a^\rho(\ \cdot\ ;\ \cdot\ )$ +4770,$\mathcal D(X)=c\mathsf{Var}(X)$ +4771,$\le$ +4772,$u''' \ge 0$ +4773,$\rho(X\wedge a)$ +4774,$Y_2$ +4775,$X=X_1+...+X_n$ +4776,$g_j$ +4777,$1 < \alpha < 2$ +4778,$\| Z \|^*= \sup\ \{ \mathsf E[YZ] \mid \| Y \| \le 1 \}$ +4779,$\alpha_i(x)=\mathsf E\left[\frac{X_i}{X}\mid X > x \right]$ +4780,$\Delta \mathit{MV}_{ro}(a)$ +4781,$\phi(s)$ +4782,$\mathsf E_{\mathbb{Q}}$ +4783,$p\cdot X$ +4784,$\mathsf E_\mathsf{Q}[X_i]$ +4785,$p_0 \le p^\ast \le p_1$ +4786,$D\rho(\cdot)$ +4787,$\lambda=0.25$ +4788,$u'''>0$ +4789,${}^nS^{-1}_X(q)\le {}^nS_Y(q)$ +4790,$S_X$ +4791,"$(\Omega, \mathcal{F})$" +4792,$S\subset\Omega$ +4793,$P_1=\mathsf E[X_1g'(S_X(X))]$ +4794,$\hat q(p) > q(p)$ +4795,$\mathsf j(a)$ +4796,$X+c$ +4797,$\Phi^{-1}(0.995)=2.576$ +4798,$S(y_j-)-S(y_j)$ +4799,"$\{\, (\mathsf E_\mathsf{Q}[X_i], \mathsf E_\mathsf{Q}[X]) \mid \mathsf Q\in\mathcal Q \, \}$" +4800,$g(p)/p$ +4801,$\mathsf E[X] \le \bar P \le \sup X$ +4802,$\alpha_2(99)=0.9$ +4803,$\alpha_iS\Delta X$ +4804,$L_0^a(X)=X\wedge a$ +4805,$\mathbf{a_{1}'}$ +4806,$g(s)=s^{0.7}$ +4807,${}^2S^{-1}(t)=q\mathsf{TVaR}_q(X)$ +4808,$\bar P_{0}=\rho(Y_{0})$ +4809,$g'(s)=\phi(1-s)\ge 0$ +4810,$\mathsf{MONO}$ +4811,$\bar M_i(a)>0$ +4812,$g(S(0-))=1$ +4813,$\rho(0)=\rho(0+0)=\rho(0)+\rho(0)$ +4814,$\rho(X_0)$ +4815,$P(\hat s)=\mathsf E[\hat s]=s$ +4816,$\delta_p/\nu_p = \iota_p$ +4817,$\mathcal{Q}=\mathcal{M}$ +4818,"$d=1,\dots,N$" +4819,$x=0$ +4820,$\mathsf{j}$ +4821,"$E_1,\dots,E_N$" +4822,$(1-p)x_0$ +4823,$U\le p$ +4824,$\mathsf E[X_i\mid X]$ +4825,"$(x_1-\epsilon,x_1]$" +4826,$\mathsf E[X] + c\mathsf E[(X-\mathsf E X)^21_{X>\mathsf E[X]}]$ +4827,$\sigma=0.15$ +4828,$pl(p)$ +4829,$g'(0)$ +4830,$P = \mathsf{VaR}_\pi(X)$ +4831,$C_i$ +4832,$x\mapsto (x-a)^+$ +4833,$h\left(\displaystyle\int_\Omega g(X(\omega))\Pr(d\omega)\right)$ +4834,$\beta_L$ +4835,$D\rho_X(X_i)$ +4836,"$\alpha_1,\alpha_2$" +4837,$\ge\mathsf E[X_i]$ +4838,$\{X>x\}$ +4839,"$x_{2,2}$" +4840,$w=1$ +4841,$F_2\prec_2 F_1$ +4842,$Z_8$ +4843,$T^{-1}(A)$ +4844,$\mathsf{TVaR}_{p_0}(X)=\mathsf E[X \mid A]$ +4845,$\sup_\mathsf{Q} (\mathsf E_\mathsf{Q}[X] - l(Q))$ +4846,$g'(s) = rs^{r-1}$ +4847,$\alpha(\mathbb{Q})=\infty$ +4848,$\mathsf{Q}\in\mathscr{M}$ +4849,$\rho(X)/2$ +4850,$ro$ +4851,$\alpha(\mathsf Q) < \infty$ +4852,$\mathsf E[(X-x)^+]$ +4853,$x_p$ +4854,$X\Delta S$ +4855,$S=e^{\mu t}$ +4856,$\Delta gS$ +4857,$s^{th}$ +4858,$\mathbf{\beta_{1}g(S)\Delta X}$ +4859,$X=X_0+Y$ +4860,$20$ +4861,$\mathsf{TI}$ +4862,$b-a$ +4863,"$\tau(a-\rho_{a,\tau}(X))$" +4864,$\rho(X) < \infty$ +4865,$Y=c$ +4866,$\rho(W_0\wedge a_0)$ +4867,$g(0.01)=0.1$ +4868,$f(x)=(x-d)^+1_{\{x \le m \}}$ +4869,$X\circ T$ +4870,"$\mu=8.7, \sigma=2.5$" +4871,$p=0.05$ +4872,$\mathit{RV}$ +4873,$\bar P(\infty)=\mathsf E[q(U)\phi(U)]$ +4874,$n=7$ +4875,$X_4=X_5=10$ +4876,$n\to \infty$ +4877,$i\not=j$ +4878,$H(x)$ +4879,$a\le \rho(X)\le b$ +4880,$EL$ +4881,"$\{\mathsf E[X_i\,Z] \mid \rho(X)=\mathsf E[XZ] \}$" +4882,$\alpha_i'(x)<0$ +4883,$q_Z$ +4884,$dp=f(x)dx$ +4885,$v_{res}\sqrt{(1+v^2)/n}\approx v_{res}v/\sqrt{n}$ +4886,$\rho(X_i)\le 0$ +4887,$s=s_1+s_2$ +4888,$\displaystyle\int_0^1 X(1-g^{-1}(1-\tilde p))d\tilde p$ +4889,$F(x_0)= p_+>p_0$ +4890,$g''(s)<0$ +4891,"$(s,m)$" +4892,$U = A = 8.149$ +4893,$P(a)da$ +4894,$B(p)$ +4895,$Q=a-P$ +4896,"$2^1, 2^3, ...$" +4897,$c(S)= \rho\left( \sum_{i\in S} X_i \right)$ +4898,$\partial f_{\bar x}/\partial x_i$ +4899,$\log(x)$ +4900,$L_d^{d+l}$ +4901,$\alpha(\mathsf Q)\not=0$ +4902,$X\le a$ +4903,$\bar P_{d}=\rho(Y_{d})$ +4904,$\kappa_i(x)/x$ +4905,$\mathsf{TVaR}_p(X)=1=\mathsf E_\mathsf Q[X]$ +4906,$D^n\rho_X(X_2)=45.1838$ +4907,$f(x)=1$ +4908,$\tilde X_1=X_1 + \mathsf E[X_2\mid X_1]$ +4909,$X_0+\epsilon Y$ +4910,$g_\tau$ +4911,$\phi'(s)ds$ +4912,$\mathsf E[Z]=1$ +4913,$g'(1)>0$ +4914,$A=8.13$ +4915,$X_n$ +4916,$\kappa_i(x) = \mathsf E[X_i \mid X=x]$ +4917,$\mathsf E[F_2]=\mathsf E[F_0]$ +4918,$a=P+Q=EL+M+Q$ +4919,$\mathit{MV}_{ro}(a_{ro})$ +4920,$g(0-)f(\esssup(X))$ +4921,$g_1$ +4922,$g'(1-p)=\nu$ +4923,$X_1+X_2=X$ +4924,$|t|$ +4925,$\rho_h(X):=\mathsf E[X_h]$ +4926,$\prec_n$ +4927,$P(X\wedge a)=\bar P(a)$ +4928,$\bar x$ +4929,$x_h>x=\mathsf{VaR}$ +4930,$1+\gamma$ +4931,$S/P$ +4932,$X_0$ +4933,$b_h$ +4934,$\mathsf P(X>a)>0$ +4935,$(1+\gamma)^{t-x}$ +4936,$n > 2$ +4937,$\sigma(X)=\mathsf E[(X-\mathsf E X)^2]^{1/2}$ +4938,$=\displaystyle\int_0^\infty x \P(\{X \in dx \})$ +4939,$\phi'(p)=f(p)/(1-p)\ge 0$ +4940,$P = \mathsf E[X] + \pi \mathsf E[(X-\mathsf E[X])^+]$ +4941,$\mathsf{VaR}_{0.98}$ +4942,$\rho(X\wedge a)=\mathsf E_\mathsf{Q}[X\wedge a]$ +4943,$\sup X$ +4944,$h_f$ +4945,$\lambda>0$ +4946,${10\choose 5} = 252$ +4947,$T$ +4948,"$i,v$" +4949,$a_i':=\sum \alpha_i(1-S)\Delta (X\wedge a)$ +4950,$\mathsf E[X]=0.6$ +4951,$u_i$ +4952,$N=40$ +4953,$\mathsf E[Z\mid X]$ +4954,$Pr(X > a)$ +4955,$X_i(a')$ +4956,$t\mapsto s(t)$ +4957,$a_{1}$ +4958,$\int_0^1 f(p)dp = 1 - \alpha < 1$ +4959,$X=q(U_X)$ +4960,$t=w$ +4961,$B=\Omega$ +4962,"$1 million auto accident, a $" +4963,$E[X_2 | X]$ +4964,$3^{20}$ +4965,$\bar S_i(x)$ +4966,$\sum_\omega Z(\omega)\mathsf{P}(\omega)=\mathsf E[Z]$ +4967,$dX$ +4968,$D\rho_X(X_1)$ +4969,"$\int_0^\infty z(x)\,dF(x)=1$" +4970,"$X_{t+1,1}$" +4971,$\log$ +4972,$(1-g(s))q$ +4973,"$(0,0,\dots,0,10)$" +4974,"$\iota, \iota(p)$" +4975,$\mathsf E_\mathsf{Q}[0]=0$ +4976,$\mathsf E X$ +4977,$\mathsf{TVaR}_{0.5}(X_2)=45.5$ +4978,$t-2$ +4979,$Z_2$ +4980,$\prec_2$ +4981,$0\le x < X_1$ +4982,$a=\sum_i a_i$ +4983,$s<0.1$ +4984,"$a(x_1,x_2)=\sqrt{3x_1^2 + 4x_2^2}$" +4985,$E[u_j(W_j - X_j + Y_j - H[Y_j])]$ +4986,$1-p=0.9$ +4987,$h(s)=1-g(1-s)$ +4988,$(P-L)/A$ +4989,$X_1(10)$ +4990,$w_0$ +4991,$AR\succ BY$ +4992,$q_X\le q_Y$ +4993,$0 < \alpha\le 1$ +4994,"$\mathsf{biTVaR}_{0,1}^w$" +4995,"$a_i=\rho(X_i, p^*)$" +4996,$\phi(p)=g'(1-p)$ +4997,$1/(1+r)$ +4998,$\dfrac{1}{1+\iota} p$ +4999,$p(1-p)$ +5000,$\rho(X) = \int_0^\infty g(S(x))dx$ +5001,$\sum S\Delta(X\wedge a)$ +5002,$V^*$ +5003,$\partial a/\partial v_1$ +5004,"$A_1=[-k,-k]$" +5005,$p=0.25$ +5006,$a^{\star}(X)$ +5007,$\mathsf E[X]+k\mathsf{Var}(X)$ +5008,$0.8 \ge p < 0.9$ +5009,$\mathcal{G}$ +5010,$g'(s-)$ +5011,$k$ +5012,$\rho(X_n) \downarrow \rho(X)$ +5013,$q_X(U)$ +5014,$wq_X(p)+(1-w)q_Z(p)$ +5015,$\mathbf{X_{2c}}$ +5016,"$p\in [0,1]$" +5017,$g(s) \approx m_0+(1+m'(0))s$ +5018,"$Y_{0,0}:=\sum_{d>0} X_{0,d}$" +5019,"$Y_m=\max(X_1,\dots,X_m)$" +5020,$\mathsf{VaR}_{0.99}(X_1)=150$ +5021,$0.01$ +5022,$\mathbf{X_2(a)}$ +5023,$\mathsf E[X_2\mid X_1]$ +5024,$\mathsf E_\mathsf{Q}[\mathsf E[X_i \mid X]]$ +5025,$\alpha_i(x) = \mathsf E[X_i /X \mid X> t]\not=\mathsf E[X_i\mid X> t]/\mathsf E[X\mid X>t]$ +5026,"$t^\star \in [0,1]$" +5027,"$\{1,2,\dots, n\}$" +5028,$a < \max(X)$ +5029,$\mathcal N_X(X_i)$ +5030,$x^{\ast}:=\min(x)$ +5031,$0.5L_{250}^{500}(x)+0.75L_{500}^{750}+L_{750}^{1000}$ +5032,"$x_0, x_1, x_2$" +5033,$\sum (1-S)\Delta (X\wedge a)$ +5034,"$[0,\infty)\subset\mathbb{R}$" +5035,$\bar Z = F(\bar x)$ +5036,$^2$ +5037,$\rho_g(X)=\mathsf E_\mathsf{Q}[X]$ +5038,$\Pr(B\le t) = 1/2 + 1_{t>1/2}(1/2)$ +5039,$q_{X}(p)=\sqrt{2}\Phi^{-1}(p)$ +5040,$a = a(\mathbf{v}) = a(X(\mathbf{v}))$ +5041,$\mathbf{\beta_{2}}$ +5042,$s=1$ +5043,$S\cdot dX$ +5044,$s$ +5045,$S(x)=u$ +5046,$\sup_{\omega\in\Omega} (f(\omega)+g(\omega)) \le \sup_{\omega\in\Omega} f(\omega) + \sup_{\omega\in\Omega} g(\omega)$ +5047,"$0,1,1,1,2,3, 4,8, 12, 25$" +5048,$\triangleright$ +5049,$\mathsf{TVaR}_p(X)=51.156$ +5050,"$A\subset [0, \infty)$" +5051,"$\Delta\,g(S)$" +5052,$\mathbf{\beta_{1}}$ +5053,$\Pr(\{\omega \mid X_n(\omega)\to X(\omega) \})=1$ +5054,$f(x)\le f(y)$ +5055,$da$ +5056,"$(\mathsf x*1.2, 2)$" +5057,$S=1$ +5058,$\rho(X)=\mathsf E_{\mathsf{Q}}[X]$ +5059,$L_{250}^{\infty}$ +5060,$\mathsf E_{\mathsf{Q}}[X_i\mid X\le a](1-g(S(a))) + a\mathsf E_{\mathsf{Q}}[X_i/X\mid X >a]g(S(a))$ +5061,$0 = x_0< x_1<\cdots < x_n < \cdots$ +5062,$\var(\sum C_i)=\sum (m_i v_i)^2 = n(mv)^2$ +5063,$\mathbf{X(a)}$ +5064,"$\nu p\,da=\nu F(a)\,da$" +5065,$\mathsf xtext$ +5066,$\hat p:=1-g^{-1}(1-p)$ +5067,"$X(x_1, x_2)=(x_1+x_2)Y$" +5068,$1-F(x)=1-p$ +5069,$\mathcal F_t$ +5070,$\rho(X)=\rho(X-Y+Y)\le \rho(X-Y) + \rho(Y)$ +5071,$c \le 0$ +5072,$S(x_{(j)})(x_{(j+1)}-x_{(j)})$ +5073,$p=0.9$ +5074,$\mathsf E[X_iZ]$ +5075,$\rho(X+Y) \le \rho(X) + \rho(Y)$ +5076,$e^{X_t}$ +5077,$n\times r$ +5078,"$f'_\omega (\bar x, h)$" +5079,"$Y_{t,d+1}$" +5080,$F(b)-F(a)$ +5081,$a_{ro}:=\mathit{VaR}_{p}(X_{-1})=10743.5$ +5082,$\rho(X) - (-\rho(-X))=\rho(X)+\rho(-X)$ +5083,$Z_\epsilon$ +5084,$\{3\}$ +5085,$L(X)=e^{kX}/\mathsf E[e^{kX}]$ +5086,$\lim_{\epsilon \downarrow 0} (f(x-\epsilon)-f(x))/\epsilon$ +5087,"$1,9,4,4,2,$" +5088,$\mathsf{TVaR}_p( X )$ +5089,$g(S)$ +5090,$\mathsf{MON}'$ +5091,$\mathsf{TVaR}_{p_1}(X)$ +5092,$1_{X < q(1-s)}-(1-g)$ +5093,$g(x)=e^{2\pi i x\theta}$ +5094,$f=f(s)$ +5095,$\mathsf E[X \mid \mathcal F_0]$ +5096,$l=a$ +5097,"$H(A, L, t)$" +5098,$\mathsf{TVaR}_{0.75}=4\left( \frac{90}{8}+\frac{98}{16}+\frac{100}{16}\right)=94.5$ +5099,$\mathit{NPV}$ +5100,$E_k$ +5101,$g(s)=s^\rho$ +5102,$X\ge 0$ +5103,$1.2\times 10^9$ +5104,$f'(a)$ +5105,$\mathsf E[f(X-\pi P)] = f((1-\pi)P)$ +5106,$y\in A$ +5107,$0 < \lambda \le 1$ +5108,"$\mathsf{cov}(X_i,X)/\sigma_X$" +5109,$t_1$ +5110,$F(x)=\Pr(X\le x)$ +5111,$\lambda>1$ +5112,$g(S(x))=g(0)=0$ +5113,$D^n\rho_{X\wedge a}(X_i)$ +5114,$\tau < t+d$ +5115,$s_2=1$ +5116,$\mathsf E_\mathsf{Q}[X_i \mid X]=\mathsf E[X_i \mid X]$ +5117,$\mathsf E[X\mid \mathcal F_t]$ +5118,$\mathsf j(a)=\max \{ j:X_j < a \}$ +5119,$g'(S(x))\ge 1$ +5120,$1-\tilde p=g(S(x))$ +5121,$F_m\succ_m F_0$ +5122,"$X_{t,d+1}$" +5123,$A(-X)=-B(X)\not=-A(X)$ +5124,$g=1$ +5125,$0.99$ +5126,$f_t$ +5127,$\mathsf{Var}^+(X)$ +5128,$\rho_X(X_i) \ge \mathsf E[X_i]$ +5129,$E[YZ]$ +5130,$1-r_0$ +5131,$\Pr(X\le x)=0$ +5132,$\lambda=0$ +5133,$\beta_2g-\alpha_2S$ +5134,$x^*$ +5135,$\lambda t$ +5136,$\{X > \mathsf{VaR}_p(X)\}$ +5137,$r_f = 0.02$ +5138,$x=1$ +5139,"$[s_0, s_1]$" +5140,$(\beta g(S))'(x)=-\kappa_i(x)g'(S(x))f(x)/x$ +5141,"$a_{0,1}$" +5142,$X_{d}$ +5143,$q(p)=\inf\{x \mid F(x)\ge p \}$ +5144,"$([0,1], \mathcal B, \mathsf P)$" +5145,$S\ge (1-\epsilon)\mathsf E[X]$ +5146,$c(1)-c(\varnothing)=c(1)$ +5147,$\rho_a(0) = \rho(0 \wedge a(0)) = \rho(0 \wedge 0) = \rho(0) = 0$ +5148,$X_1=\mathsf E[X\mid \mathcal F_1]$ +5149,$\rho(X)\le \rho(\lambda X)/\lambda$ +5150,$c(\sum_{i\in S} X_i)$ +5151,$g(0)=0$ +5152,$\alpha_{1}$ +5153,$\var(\sum C'_i)=v_{res}^2 \sum c_i^2$ +5154,$0 < b \le 1$ +5155,$pX + (1-p)Z$ +5156,$\pi(X)$ +5157,$\mathsf E[Y \mid U]$ +5158,$\Pr(X>a)$ +5159,${}^nS^{-1}(q)$ +5160,$\sup X=\inf$ +5161,$Q^*$ +5162,$v-\nu^{\star}=(\iota^{\star}-i)/v\nu^{\star}$ +5163,$_{ro}$ +5164,$\iota=\delta/\nu$ +5165,$m'(1) = -m_2/(1-s_2)$ +5166,$D^n\rho_{X\wedge a}(\cdot)$ +5167,$(M-N)\times d$ +5168,$S(x_0)=1$ +5169,$10/11$ +5170,$f(L)=(L-a)^+$ +5171,$\mathsf{j}(a) = \max\{ j:X_j < a \}$ +5172,"$3.807=\lambda \sigma(W_{0,0})$" +5173,$\bar P(a)>\mathsf E[X\wedge a]$ +5174,$\mathsf E[X]=k/(k+\beta)$ +5175,"$\mathsf E[X_{t,d}\mid \mathcal F_{\tau}]$" +5176,$h(x)=\sqrt x$ +5177,$ for $ +5178,$S(x-)=1$ +5179,$\{ Z\not=0 \}$ +5180,$\iota=(g(s)-s)/(1-g(s))$ +5181,$\tau=0$ +5182,$(r-i)Q_t$ +5183,$\delta p$ +5184,$\mathsf{TVaR}_p = q(p)$ +5185,$\sigma=0.1980$ +5186,$X_1> x_1$ +5187,$\mathsf E[X\mid t+d]$ +5188,$1/(1-p)>1$ +5189,$\mathsf E_{\mathsf{Q}}[(X-a)^+] \le \rho((X-a)^+)$ +5190,$q_V(p)=0$ +5191,$(1-s)^{-1/2}/4$ +5192,$\mathsf E[p]\not=1$ +5193,$g(0-)$ +5194,$(s+\iota) / (1+\iota)$ +5195,${}^2S(t)=\mathsf E[(X-t)_+]$ +5196,$k = 1.4 + 1.8s$ +5197,$\Psi(x)=1-\exp(-e^x)$ +5198,$=\displaystyle\int_0^\infty S(x)dx$ +5199,$dp$ +5200,$da\to 0$ +5201,"$(lee.east |- lee.north)+(0.25,0.25)$" +5202,$G$ +5203,$X'=0$ +5204,$\rho_g$ +5205,$s > 0.5$ +5206,$\Pr(M=m)=\frac{r}{1+r}\frac{1}{(1+r)^m}$ +5207,$\rho=0.12$ +5208,$\beta_1g(S)dx$ +5209,$X(x)=x$ +5210,$g(S(x)) = S(x) + \delta(F(x))F(x)$ +5211,$L_X \in \mathcal L_\rho$ +5212,$g-S$ +5213,$x_0$ +5214,$\mathbf{a}$ +5215,$0=\rho(0)$ +5216,$Xm1=X_{-1}$ +5217,$\mathsf E[X\mid \mathcal F_{\tau}]$ +5218,$1-g^{-1}(1-p')$ +5219,$\alpha_i(x)S(x)=\mathsf E[(X_i/X)1_{X>t}]$ +5220,$\mathsf E[kX]=k\mathsf E[X]$ +5221,$B(1_{U>0.95})=B(1_{U\le 0.05})=h(0.05)=1-g(1-0.95)=0.0203$ +5222,$\phi(p)\ge 0$ +5223,$E(X_{-1}\wedge a)$ +5224,$n=8$ +5225,$R/Q$ +5226,$q < p$ +5227,$x=wy + (1-w)z$ +5228,"$B_3=[-k, \epsilon]$" +5229,$Q = 5.0449$ +5230,$\rho(X)=\max_k \mathsf E_{\mathsf Q_k}[X]$ +5231,$n'=7$ +5232,$g'(t)>0$ +5233,"$j=0,\dots, N-1$" +5234,$0\ < p < 1$ +5235,$(S_t-a)^+$ +5236,$\alpha+\beta = \iota^\ast/(1+\iota^\ast)$ +5237,$\sin(x)$ +5238,$\mathbf{P_i}$ +5239,$a_{gc}:=\mathit{VaR}_{p}(X)={{a_x}}$ +5240,$\mathsf{VaR}_{0.995}$ +5241,$P(X_{-1}(a_{gc}))={{mvp_gc}}$ +5242,$\rho''(x)=-U''(x)>0$ +5243,$\{\omega\mid X(\omega)=x\}$ +5244,$\tilde M_i(a) = \bar P_i(a) - \mathsf E[X_i(a)]$ +5245,$\kappa$ +5246,$\mathsf E[X_i \mid X=q(1-g^{-1}(1-p))]$ +5247,$e$ +5248,$\omega'=\omega$ +5249,$0.3 < s <0.4$ +5250,$g(s)=s^\alpha$ +5251,$X_1-X_2$ +5252,$a = \sum_i a_i$ +5253,$\rho(X)=\mathsf{VaR}_{0.995}(X)-\mathsf E[X]$ +5254,$\rho(X)=1$ +5255,$H(X)\le H(Y)$ +5256,$Y=X$ +5257,$\{\omega\in \Omega \mid (X\wedge a)=a \}$ +5258,$X\ge x_0$ +5259,$r=1$ +5260,"$\bar Q_{0,1}$" +5261,$Y\preceq_2 X$ +5262,$\rho(X)=k\mathsf{Var}(X)$ +5263,$\delta = \iota\nu$ +5264,$g'(1-s)=\phi(s)$ +5265,$q(U_X) < m$ +5266,$\alpha_1$ +5267,$A(X+Y)\le A(X)+A(Y)$ +5268,"$a_{0,t}' = a_{0,t}$" +5269,"$j=5,6$" +5270,$\mathsf Q_k$ +5271,$\lambda < 1$ +5272,$\mathcal E:=\{Y \circ T \mid T \text{ PPT} \}$ +5273,$Xp$ +5274,"$(lee.east |- lee.south)+(0.375,-0.25)$" +5275,$dF=-dS=$ +5276,$m(s) := (1-s)\wedge m(s)$ +5277,$\mu_{rU} = M/K = 0.133$ +5278,$y \wedge (x-a)^+$ +5279,$\mathcal A=\{X\mid \rho(X)\le 0 \}$ +5280,"$Y_{0,0}$" +5281,$\bar P_{1}$ +5282,$\alpha_1+\alpha_2=\beta_1+\beta_2=1$ +5283,$\mathbb{Q}'(\Omega_a) =\mathbb{Q}(\Omega_a)$ +5284,$a_l>b_l$ +5285,$X_0=0$ +5286,$\mathsf E[X\mid \mathcal F_t](\omega)=\sum_{i \le t} \omega_i/2^i+2^{-(t+1)}$ +5287,$\Delta Q_{gc}(a)$ +5288,$P_j=\sum_{i=0}^j p_i$ +5289,$\{y_j\}$ +5290,$X=3$ +5291,$\rho(X)=\bar P$ +5292,$\alpha(\mathsf Q)\ge 0$ +5293,$\mathsf E_{\mathsf{Q}}[X_i \mid X]$ +5294,$a_l$ +5295,$A$ +5296,$v(AB) + v(ABCD) = 3/2 > v(ABC) + v(BCD) = 4/3$ +5297,$\sum p_jX_j$ +5298,$\Pr(\{\omega_1\})=1/3$ +5299,$0.5+U/4$ +5300,$\mathbf{\alpha_2S\Delta X}$ +5301,$n=3$ +5302,$\bar\nu$ +5303,$p^*=1$ +5304,$r_K = \exp (\lambda) - 1$ +5305,$x<1$ +5306,$a(X)=a(\sum_i X_i) = \sum_i a_i$ +5307,$P(X_{-1}(a))=\bar P^a_0$ +5308,$\kappa_{1}$ +5309,$\{\omega\in\Omega \mid X(\omega) \le x\}\in\mathcal F$ +5310,$\mathsf{TVaR}_{0.6975}$ +5311,$F(q^-(p))=p$ +5312,$\mathsf E[XZ_j] = (5)(1/10)(8)+(5)(1/10)(9)=8.5=\mathsf{TVaR}_{0.8}(X)$ +5313,$B_2 \succ A_2$ +5314,$\hat{s}$ +5315,$\rho(X+\rho(X))=\rho(X)-\rho(X)=0$ +5316,$\mathsf{NORM}$ +5317,$Y\succeq X$ +5318,$\lim_{x\to\infty} xg(S(x))=0$ +5319,$\int xdF$ +5320,$t > 2/3$ +5321,$p=1-s_j$ +5322,$P_2\ge (\rho(X_1)-P_1) + \rho(\mathsf E[X_2\mid X_1])\ge \rho(\mathsf E[X_2\mid X_1])$ +5323,"$d,v\ge 0$" +5324,$X_1\le X_2$ +5325,$r_D$ +5326,$x=\max(X)$ +5327,$\rho(\tilde X_1)=\rho(X_1)+\rho(\mathsf E[X_2\mid X_1])$ +5328,$c=0$ +5329,$1/\lambda = \sum_j 1/\lambda_j$ +5330,$>0$ +5331,$\rho_a(X)>2\rho_a(X_1)$ +5332,$Z(200)=0$ +5333,$A=\{X>x\}$ +5334,$\mathsf E[Y_{d}]=\sum_{s>d} \mu_s$ +5335,$n\ge 0$ +5336,$\mathsf E[X_i(x)]$ +5337,$\bar P(a)\le a$ +5338,$\displaystyle\int_0^\infty g(S(x))dx$ +5339,$M(x)$ +5340,$\int_0^1 F^{-1}(p)dp$ +5341,$e_x=\sum_t {}_tp_{x}$ +5342,$g'\left (S_{X\wedge a}(X\wedge a)\right )$ +5343,$0 < g' \le 1$ +5344,$\mathit{NPV}_1$ +5345,$\bar F(a)=\int_0^a F(x)dx = a-\bar S(a) = \bar Q(a) + \bar M(a) = \mathsf E[(a-X)^+]$ +5346,$0.75+U/4$ +5347,$g_2$ +5348,$r_D=0$ +5349,$\displaystyle\int_\Omega X(\omega)\P(\omega)$ +5350,$p:=1-s$ +5351,$\bar\delta=\bar\iota\bar\nu$ +5352,$\rho(X)=\sup_{\mathsf Q\in\mathcal Q} \mathsf E_\mathsf{Q}[X]$ +5353,$\rho(aX)=a\rho(X)$ +5354,$P=\mathsf E[X]$ +5355,$f(x-)$ +5356,$A_i\cup A_i^c$ +5357,"$(s_0,g(s_0))$" +5358,$Q_0=0.25$ +5359,$3$ +5360,$X=\sum_t B_t/2^i$ +5361,$\iota(s)=(1-s)/(1-1)=\infty$ +5362,$Z_A=(1-p)^{-1}1_A$ +5363,$Q\circ T\in\mathcal{Q}$ +5364,$\mathsf E_{\mathsf Q}[X_i \mid X=x] = \mathsf E[X_iZ \mid X=x]/\mathsf E[Z \mid X=x] = \mathsf E[X_i \mid X=x]$ +5365,$\mathcal Q$ +5366,$t>\tau$ +5367,$w$ +5368,$\Delta X_j=X_{j+1}-X_j$ +5369,$\mathsf E[X_i \mid X = x]$ +5370,$1-g(S(t))$ +5371,$\mathbf{a_1'}$ +5372,$ to be the set of all sample points where the insurance event $ +5373,$1-1_{X>a}=1_{X\le a}$ +5374,$s=1-p$ +5375,$f(x)=x$ +5376,$\rho(X)=\mathsf E_{\mathbb{Q}}[X]$ +5377,$s \approx 0$ +5378,$j=9$ +5379,$k\le m$ +5380,$\epsilon$ +5381,$\bar Q(a)=a-\bar P(a)$ +5382,$#2$ +5383,$\rho(X) = \mathcal{N}_{\tilde X}(X)$ +5384,$p$ +5385,$3/4 \pm 1/4$ +5386,$10^{-2}$ +5387,$\mathcal B$ +5388,$\epsilon>0$ +5389,"$g(s) = \nu s + \delta, s>0$" +5390,$\rho(X) = \max_{\mathsf Q\in \mathcal Q} \ \mathsf E_\mathsf{Q}[X]$ +5391,$X(\omega)\ge a'$ +5392,$r=0.025$ +5393,$\{X=q_X(p)\}$ +5394,$m$ +5395,$\mathcal F_0$ +5396,$\alpha_i(x) = \mathsf E[X_i /X \mid X> x]\not=\mathsf E[X_i\mid X> x]/\mathsf E[X\mid X>x]$ +5397,$L_0$ +5398,$m\le 4$ +5399,$\mathsf{TVaR}_1(X)=\sup(X)$ +5400,$q(p)=\mathsf{VaR}_{p}(X)$ +5401,$\rho(X-Y)\le 0$ +5402,$\mathbf{d=0}$ +5403,$P_{i}(a)$ +5404,$\rho(X)=\mathsf{TVaR}_p(X)$ +5405,$\mathsf E[X]=\mathsf E[Y]$ +5406,"$\mathbf{v}=(v_1,v_2)$" +5407,$\kappa_i(t)=E[X_i \mid X=t]$ +5408,"$(s, g(s))$" +5409,"$(-1,1)$" +5410,$X'=\mathsf E[X\mid A]$ +5411,$\mathsf E[X]+\mathsf{SD}(X) \le \mathsf E[Y]+\mathsf{SD}(Y)$ +5412,$n\times 1$ +5413,$g'(S(x))<1$ +5414,$X_{1}$ +5415,$\rho(X)\le\lim \rho(X_n)$ +5416,$\mathsf{TVaR}_0(\cdot)=\mathsf E[\cdot]$ +5417,$q^+(p) := \sup\ \{x \mid F(x) \le p \} = \inf\ \{ x \mid F(x) > p \}$ +5418,$M-N$ +5419,"$i=2,3,4,5$" +5420,$\mathsf E[Z_j\mid X]$ +5421,$X_i(v_i)=v_iX_i(1)$ +5422,$X\le Y$ +5423,$S\Delta X'$ +5424,$\rho(X\wedge a)=0.909$ +5425,$(1+\gamma)F_0$ +5426,$\sigma=\sqrt{s(1-s)/N}$ +5427,$\iota(s)$ +5428,$a-\bar P(a)$ +5429,$F^{-1}$ +5430,$\mathsf E[X] + \pi \mathsf E[(X-\mathsf E[X])^+]$ +5431,$\kappa_2(X)$ +5432,$U$ +5433,"$Y_{t,1}$" +5434,"$k=1,2,\dots,n-1$" +5435,$1/(1+r_f) = \mathsf E[p]$ +5436,$g(S(x-))=1$ +5437,$X_0 + \epsilon Y$ +5438,"$\displaystyle\int_0^a \kappa_i(x)g'(S(x))f(x)\,dx + a\beta_i(a)g(S(a))$" +5439,$\kappa_i(x) = \mathsf E[X_i \mid X=x]=\mathsf E_{\mathsf Q}[X_i \mid X=x]$ +5440,$m(s)$ +5441,$x_0 \ge q^-(p)$ +5442,$X(\mathbf{v}) = \sum_i X_i(v_i)$ +5443,$a=9532.0$ +5444,$L_{250}^{1000}(x)$ +5445,"$\sigma=13,108$" +5446,$T_2 := ((n+1)-pN)x_n$ +5447,$\{ X>x \}$ +5448,$\iota = \dfrac{g(s)-s}{1-g(s)}$ +5449,$\Pr$ +5450,$S_{\mathbf{v}}(t)=\text{Pr}(X({\mathbf{v}})>t)$ +5451,$g(s) = s^r$ +5452,$\Delta X$ +5453,$=$ +5454,$R^2$ +5455,$S(x_4)$ +5456,$S_X(x) \ge S_{X_1}(x)$ +5457,$X+100$ +5458,"$\Omega=\{0,1,2,\dots \}$" +5459,$\kappa\ge K(n)=\sum_s n_s(1-g(s))k(s)$ +5460,$R(X)$ +5461,$g(S_6)\Delta X'_6$ +5462,$\rho(X-\rho(X))=0$ +5463,$g(0+) > 0$ +5464,"$X_i,X$" +5465,$p=0$ +5466,$r_h=\mu_L=0$ +5467,$g(0^+)>0$ +5468,$\mathrm{Pr}_{rn}\{P_{act}>P\}$ +5469,$\{ Z\mid \rho(X)=\mathsf E[XZ] \}$ +5470,"$(I, \mathcal B, \mathsf P)$" +5471,$\mathbb{R}^3$ +5472,$ is not continuous and $ +5473,$E'=\Omega\setminus E\in\mathcal F$ +5474,$a_x$ +5475,"$\{1,2,\dots,10000\}$" +5476,$\Pi$ +5477,$\mathsf E X + c\mathsf E[\vert X-\mathsf E X \vert^p]^{1/p}$ +5478,$ipl(p)$ +5479,$a'(x)=a(1)$ +5480,$-g''(t) = w \delta_{\alpha_1}/\alpha_1 + (1-w) \delta_{\alpha_2}/\alpha_2$ +5481,$\mathsf E[X\mid X\ge \mathsf{VaR}_p(X)]$ +5482,$a=\infty$ +5483,$\bar P_g$ +5484,$\sum_i a_i=\sum_i a(X_i;X)=\rho(X)$ +5485,$a^\rho$ +5486,$p_{\mathit{cl}}$ +5487,$h(1)=1$ +5488,$\mathbf{\omega_i}$ +5489,$\Delta_{1}$ +5490,$p^+=\mathsf P(X\le q_X(p))$ +5491,$\rho=\dfrac{M}{l} = \dfrac{1-\lambda}{\lambda}$ +5492,$\rho_1$ +5493,$S_{\mathbf{v}}(a)$ +5494,$^\circledR$ +5495,$\Pr(X>x)$ +5496,"$g(s)=\min(g_1(s), g_2(s))$" +5497,$a(X)=\mu+4\sigma$ +5498,$S\approx \mathsf E[X]$ +5499,$\mathbf p$ +5500,$\mathsf E[Y\mid\mathcal F']=\mathsf E[Y]$ +5501,$pq$ +5502,$\rho(X+Y)=\rho(X) + \rho(Y)$ +5503,$\mathsf x\mathsf{VaR}_p(X):=\mathsf{VaR}_p(X)-\mathsf E[X]$ +5504,$\Pr(q^-(F(X))\not=X)=0$ +5505,$g'=2/3$ +5506,$X\wedge a\Delta g$ +5507,$P=80$ +5508,$\rho(-H)=\rho(C)-1=-0.05$ +5509,$i$ +5510,$S_i(x)=\alpha_i(x)S(x)$ +5511,$X'(\omega) \le Y'(\omega)$ +5512,$B_t(\omega)=\omega_t$ +5513,$S(x)/P(x)$ +5514,$\mathbf{j}$ +5515,"$\int_0^s g'(t)\,dt=\nu s$" +5516,$L_X(v)=l(v)$ +5517,$\mu=\log(\theta)$ +5518,$\Pr(X > q_{\mathbf{v}}(p))=1-p$ +5519,$T_{(1)}=W$ +5520,$t\in\mathbb{R}$ +5521,"$(x_{1,i}, x_{2,k(i)})$" +5522,$\rho_g(X\wedge a)=\bar P(a)$ +5523,$g'>0$ +5524,$X\wedge a = \sum_i X_i(a)$ +5525,$t=-\log(1-p)$ +5526,$S_X(y)$ +5527,$\mathsf E[X\mid X=x]\equiv x$ +5528,$\sum_i x_i\Pr(X=x_i)$ +5529,$n=2^m+k$ +5530,$\mu t$ +5531,"$1/2, 1/4$" +5532,$\mathsf{CX}$ +5533,$\sigma^2 = \sum \sigma_i^2$ +5534,$\iota=M/Q$ +5535,$AB$ +5536,"$\displaystyle\int_0^a \beta_i(x)g(S(x))\,dx$" +5537,$\bullet$ +5538,$366.4$ +5539,"$\tilde X:[0,\infty)\to[0,\infty)$" +5540,$1-\alpha_i(t)S(t)$ +5541,$F_1$ +5542,$a=\mathsf{VaR}_p$ +5543,$(a'-X)^+$ +5544,$(\alpha_i S)'(x)=-\mathsf E[X_i\mid X=x]f(x)/x=-\kappa_i(x)f(x) / x$ +5545,$\mathbf{X_1pK}$ +5546,$\mathsf{FSD}$ +5547,$a={{a_x}}$ +5548,"$(0.2, 0.304)$" +5549,$e^{\mu_A}-1$ +5550,$-\rho(X-Y)\le \rho(Y)-\rho(X)$ +5551,$B^c_k$ +5552,$-$ +5553,$d+l$ +5554,$0.1005$ +5555,$r_i$ +5556,$\bar\delta a$ +5557,$c > 1/2$ +5558,"$\mathsf{PML}_{n, \lambda}(X)=\mathsf{PML}_{n, \lambda}$" +5559,$f(x)$ +5560,$h(1-p)=1-g(p)=1-\sqrt{0.9}=0.051$ +5561,$\mathbf{x}$ +5562,$Gn$ +5563,$\mathcal F$ +5564,$g_2(s)=\sqrt{s}$ +5565,$\bar P_0>\mathsf E[Y_{0}]$ +5566,$v_f=1/(1+r_f)$ +5567,$B\subset \Omega$ +5568,$\bar S(x)$ +5569,"$s_j,g_j\in[0,1]$" +5570,$\mu=21.315$ +5571,$a_{gc}=P(X_{-1}(a_{gc}))+P(X_{0}(a_{gc}))+\mathit{MV}_{gc}(a_{gc})$ +5572,$X0=X_{0}$ +5573,$X=(X\wedge a) + (X-a)^+$ +5574,$\mathsf E[L\wedge A]$ +5575,$(\mathsf{TVaR}_p - q(p))/(1-p)$ +5576,$X \preceq_n Y$ +5577,$\lambda_i$ +5578,$\mathsf{VaR}_{0.95}(X)=3395$ +5579,"$W_2=\sum_{t+d=2} Y_{t,d}$" +5580,$a\ge \sup(X)$ +5581,$a=Q+R$ +5582,$p/q-1=(p-q)/q>0$ +5583,$\alpha_1\ge \beta_1$ +5584,"$c_1=(c(1) + c(1,2)-c(2))/2$" +5585,$\Pr(X > a) \le \epsilon$ +5586,$Z\in D\rho(X_0)$ +5587,$\cdots$ +5588,$d\bar S(a)/da$ +5589,$\omega'=0$ +5590,$\rho(Y)=g(pq)$ +5591,"$\phi(s) = (1-p)^{-1}1_{[p, 1]}(s)$" +5592,$dg/ds$ +5593,$T_1 := X_{n+1} + \cdots + X_{N-1}$ +5594,$\kappa_i(x)=\mathsf E[ X_i \mid X = x]$ +5595,$\displaystyle\int_0^\infty xd(g\circ F)(x)$ +5596,$\mathsf{POS\ LOAD}$ +5597,$R_x$ +5598,$t\mapsto W_t$ +5599,$\mu+\lambda\sigma$ +5600,$\rho(X)\le\rho(0)=0$ +5601,$\kappa_2$ +5602,$k(i)$ +5603,$\chi( s ) = p - \log(s)$ +5604,$C$ +5605,$0\le x\le 1000$ +5606,"$\Omega=(0,1)$" +5607,$\mathsf E[X_iZ]=500$ +5608,$\mathsf E[X_i (X\wedge a)/X \mid X=x] = \mathsf E[X_i\mid X=x] (x\wedge a)/x$ +5609,$D(t)$ +5610,$w(x)=x$ +5611,$Z(X)$ +5612,$1 < x < 2$ +5613,$P/A$ +5614,$\mathsf{TVaR}_{p^*}(X_1)+\mathsf{TVaR}_{p^*}(X_2)=80$ +5615,$g(S(x))$ +5616,$s<0.20$ +5617,$M_i = \beta_ig-\alpha_iS$ +5618,"$[0,1,\dots,n]$" +5619,$a(X_i;X)\ge \mathsf E[X_i]$ +5620,$X\Delta g(S)$ +5621,$\mathsf Q\not\ll \mathsf P$ +5622,$q(p')=q(p)$ +5623,$\mathsf E[XZ_\epsilon]\to \mathsf E[XZ]$ +5624,$100G$ +5625,$g(x)$ +5626,$c-1$ +5627,$\mathbf{\Delta(X\wedge a)}$ +5628,$\lambda$ +5629,$C^1$ +5630,$q^-(F(x))\le x$ +5631,$h(p)p$ +5634,$a=f=1$ +5635,$R_L=(L-P)/P$ +5636,$\omega\mapsto \psi=F(X(\omega))$ +5637,$r-i$ +5638,$\sigma=0.4$ +5639,$y$ +5640,$d>0$ +5641,$\mathsf{TVaR}_p(X)= \sum_i X_iZ_i / 10$ +5642,$F_0=2$ +5643,$\rho(X+c) = \rho(X)+c$ +5644,$X\ge X+Y$ +5645,$X > x$ +5646,$c(X(\mathbf v))$ +5647,$\mathsf E_\mathsf{Q}[X_i \mid X=x]=\mathsf E[X_i g'(S(X))1_{\{X=x\}}] / \mathsf E[g'(S(X))1_{\{X=x\}}] = \mathsf E[X_i1_{\{X=x\}}]/\mathsf E[1_{\{X=x\}}]=\mathsf E[X_i\mid X=x]$ +5648,$\beta-\alpha$ +5649,"$(1+t)(1), (1+t)(2),\dots,(1+t)(10)$" +5650,$q = 1-p$ +5651,$\rho_g(X)=g(s)$ +5652,$\Delta_d=a_{d}'-a_{d}$ +5653,$\kappa_1$ +5654,$\mathsf E_\mathsf{Q}[X+c]=\mathsf E_\mathsf{Q}[X]+c$ +5655,$_{gc}$ +5656,$q(p')$ +5657,$f_i(x+y)=f_i(x)+f_i(y)$ +5658,$=\mathrm{MV}(T(X))$ +5659,$F(a-)=\lim_{x\uparrow a} F(x)$ +5660,$\int_\Omega X(\omega)\mathsf \Pr(d\omega)$ +5661,$g(S(x))>S(x)$ +5662,$s_0/2^{n}$ +5663,$\alpha f/(1-g)$ +5664,"$a_i=a(X_i, p^*)$" +5665,$\Delta X=X_1$ +5666,$V(U)$ +5667,"$f(x)=\int_0^1 f'(tx)\,dt$" +5668,$9$ +5669,$\mathsf E_{\mathsf Q}[X_i\mid X\le a](1-g(S(a))) + a\mathsf E_{\mathsf Q}[X_i/X\mid X >a]g(S(a))$ +5670,$S_{X_{-1}}(a)$ +5671,$S(y_j-)-S(y_j) =\Pr(X=y_j)$ +5672,$g(S_4)=0.5$ +5673,$S(x)>0$ +5674,$q(1)$ +5675,$x_{max}$ +5676,$a \ge 0$ +5677,$E[s|t]=0.08353$ +5678,$ag(S_{\mathsf{j}(a)})=(80)(0.5)=40$ +5679,$\rho(\tilde X\wedge a)\le a$ +5680,$\preceq$ +5681,$X'$ +5682,"$\mathsf{NORM,TI}$" +5683,"$X^+=\max(X,0)$" +5684,$h(s) < s$ +5685,$\mathsf E[X] + \pi \mathsf{SD}(X)$ +5686,$g(s)>s$ +5687,"$(s,g)$" +5688,$1_{U V(2)$ +5707,$\mathbf{Q=1-g(S)}$ +5708,$\mathsf E[Z_i\mid X] \ne \mathsf E[Z_j \mid X]$ +5709,$v_f(\mathsf E_\mathsf{Q}[X_i] - \mathsf E_\mathsf{Q}[X_i/X(X-a)^+])$ +5710,$D = L^* - L$ +5711,$Z_\mathit{lift}$ +5712,$\pi_1$ +5713,$p<0.01$ +5714,$f(s)$ +5715,$\mathbf{\rho(X\wedge a)}$ +5716,$\mathsf E[Z \mid X]\preceq_2 Z$ +5717,$\lambda X_1$ +5718,$\mathsf E[X]$ +5719,$h(X)$ +5720,$\rho_2(X_i)=0.5$ +5721,$Wx)=1-F(x)$ +5725,$\rho(X_n(t))$ +5726,$\int xf(x)dx$ +5727,$\mathsf E_\mathsf{Q}[X+tY]$ +5728,$\tau=0.156$ +5729,$\mathsf{VaR}_p(X) = \mathsf E[X] + \pi(X)\mathsf{SD}(X)$ +5730,$\log(\mathsf E[e^{\pi X}])/\pi$ +5731,"$t=2,3,\dots$" +5732,"$f:[0,1]\to\Omega$" +5733,"$x=x(A,L)=A/L$" +5734,$F(x)=p$ +5735,$X_2=c$ +5736,"$\mathbf{g(S)\, \Delta X}$" +5737,$\sum_{i} X_i(a) = X\wedge a$ +5738,$M = 0.6054$ +5739,$s^\ast = 1/2$ +5740,$W_j$ +5741,$a=\mathsf{TVaR}_p(X)$ +5742,$g(s)=1\wedge(s/0.35)$ +5743,$g'(s)=\alpha s^{\alpha-1}$ +5744,"$\mathbf{\omega_1},\dots,\mathbf{\omega_n}$" +5745,$\mathsf{TVaR}_{p_0}(X)$ +5746,"$A,B\subset \Omega$" +5747,$1/p$ +5748,$F_0$ +5749,$n/(n-1)=1/p$ +5750,$\displaystyle\int_0^\infty S(x)dx$ +5751,$a=\mathsf{VaR}_{1-g^{-1}(\tau)}(X)$ +5752,$(X(\omega_1)-X(\omega_2))(Y(\omega_1)-Y(\omega_2))\ge 0$ +5753,$ROE=-m'(1)/(1-m'(1))$ +5754,$\mathbf{F(x)=\Pr(X\le x)}$ +5755,$\delta>0$ +5756,$\mu(\{\alpha \})=1$ +5757,$\mathsf{Var}(U)>\mathsf{Var}(X)$ +5758,"$Y_{t,d=0}$" +5759,$(l-X)^+$ +5760,"$\rho(X)=\max(\rho_1(X), \rho_2(X))$" +5761,$9/6$ +5762,$j=2$ +5763,$\rho_1(X_i)=1$ +5764,$D^n\rho(\cdot)$ +5765,$\mathsf{FATOU}$ +5766,$p_0$ +5767,$\bar P=\bar P_1+\bar P_2$ +5768,$\mathsf{CTE}_p(X)=(12+25)/2=18.5$ +5769,$\rho(\tilde X_1)=\rho(X_1) + \mathsf E[X_2]$ +5770,$f=1$ +5771,$U_X = F(X-) + V(F(X) - F(X-))$ +5772,$ROL = EL + \lambda (\mathit{EL} (1 - \mathit{EL})/w)^{1/2}$ +5773,$q$ +5774,$v_{res}$ +5775,"$\{1,\dots,n \}$" +5776,$\Pr(X < x)=1/6=\Pr(X\le x)$ +5777,$\mathsf E_{\mathsf Q}[.]$ +5778,$\mathit{MV}_{gc}(a_{gc})=a_{gc}-P(X\wedge a_{gc})=5583.9$ +5779,$q_Y(U)$ +5780,$x^{\ast}$ +5781,$g''(s)=-s^{-3/2}/4$ +5782,$d\tilde p=g'(S(x))f(x)dx$ +5783,$N\times 1$ +5784,$F_X$ +5785,$\mathsf E[X]+\lambda\sigma(X)$ +5786,$\preceq_n$ +5787,$s \to 0$ +5788,$A\subseteq \Omega$ +5789,$r =$ +5790,$t=1$ +5791,"$(s_i,m_i)$" +5792,$F_X(x)\ge F_Y(x)$ +5793,$g'''>0$ +5794,$T=1$ +5795,$\mathsf x\mathsf{VaR}$ +5796,$\mathsf E X + c{(X-\mathsf E X)^+}_p$ +5797,$\mathcal F_{\tau}$ +5798,"$\mathbf X = (X_1, \dots, X_n)$" +5799,$\bar P_{act} = \bar P + F_0 > \bar P$ +5800,$(f)$ +5801,$y^2 - 2\sigma y=(y -\sigma)^2 -\sigma^2$ +5802,"$[0,t]$" diff --git a/greater_tables/words-12.md b/greater_tables/words-12.md new file mode 100644 index 0000000..46006ad --- /dev/null +++ b/greater_tables/words-12.md @@ -0,0 +1,25912 @@ +aaron +aback +abacus +abandon +abandoned +abandoning +abandonment +abandons +abated +abba +abbas +abbot +abbott +abbreviate +abbreviated 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Table 1

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indexlevel_0level_1202520262027
0GAAPUnderwriting Result-394.81
1GAAPNet Investment Income60.5266.57
2GAAPOperating Result-334.2966.57
3GAAPDividends
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Table 2

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Some text above the table.

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Table 1. A table with varied column widths.
ABC
years!IntFloatFloat3Longer Text
2000-100,000 2.389p-1,601.002025-03-14once upon a time, once upon a time, once upon a time, once upon a time
2001-91,667 22.217p-1,367.622025-03-26 risk is hard to define
2002-83,333 206.619p-1,134.252025-04-07 not in Kansas anymore
2003-75,000 1.922n-900.882025-04-19 neutrinos are hard to detect
2004-66,667 17.870n-667.502025-05-01 Adam Smith is the father of economics
2005-58,333 166.196n-434.122025-05-13once upon a time
Footer 1 stuff. This is very long. This is very long. This is very long. This is very long. Footer 2 stuff.
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All Tables Test - New TestDFGenerator test_suite

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Author
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Stephen J. Mildenhall

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March 14, 2025

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from IPython.display import HTML, display
-import matplotlib as mpl
-import matplotlib.dates as mdates
-import matplotlib.pyplot as plt
-import numpy as np
-import pandas as pd
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-import greater_tables as gter
-import greater_tables.utilities as gtu
-from greater_tables import GT, sGT
-gter.logger.setLevel(gter.logging.WARNING)
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…code build completed.

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1 A Hard-Rules table

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Second level index has mixed types. Range of magnitudes. Picking out years.

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level_1 = ["A", "A", "B", "B", 'C']
-level_2 = ['Int', 'Float', 'Float', 3, 'Longer Text']
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-multi_index = pd.MultiIndex.from_arrays([level_1, level_2],
-        names=["Level 1", "Level 2"])
-start = pd.Timestamp.today().normalize()  # Today's date, normalized to midnight
-end = pd.Timestamp(f"{start.year}-12-31")  # End of the year
-
-hard = pd.DataFrame(
-{'years!': np.arange(2000, 2025, dtype=int),
-'a': np.array(np.round(np.linspace(-100000, 100000, 25), 0), dtype=int),
-'b': 9.3 ** np.linspace(-12, 12, 25),
-'c': np.linspace(-1601, 4000, 25),
-'d': pd.date_range(start=start, end=end, periods=25),
-'e': ('once upon a time, risk is hard to define, not in Kansas anymore, '
-        'neutrinos are hard to detect,  '
-        'Adam Smith is the father of economics'.split(',') * 5)
-}).set_index('years!')
-# hard = hard.head()
-hard.columns = multi_index
-hard
-
-
-
-
-Table 1: Default display output (Quarto generated caption) -
-
-
-
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Level 1ABC
Level 2IntFloatFloat3Longer Text
years!
2000-1000002.388937e-12-1601.0002025-03-14 00:00:00once upon a time
2001-916672.221711e-11-1367.6252025-03-26 04:00:00risk is hard to define
2002-833332.066191e-10-1134.2502025-04-07 08:00:00not in Kansas anymore
2003-750001.921558e-09-900.8752025-04-19 12:00:00neutrinos are hard to detect
2004-666671.787049e-08-667.5002025-05-01 16:00:00Adam Smith is the father of economics
2005-583331.661955e-07-434.1252025-05-13 20:00:00once upon a time
2006-500001.545619e-06-200.7502025-05-26 00:00:00risk is hard to define
2007-416671.437425e-0532.6252025-06-07 04:00:00not in Kansas anymore
2008-333331.336805e-04266.0002025-06-19 08:00:00neutrinos are hard to detect
2009-250001.243229e-03499.3752025-07-01 12:00:00Adam Smith is the father of economics
2010-166671.156203e-02732.7502025-07-13 16:00:00once upon a time
2011-83331.075269e-01966.1252025-07-25 20:00:00risk is hard to define
201201.000000e+001199.5002025-08-07 00:00:00not in Kansas anymore
201383339.300000e+001432.8752025-08-19 04:00:00neutrinos are hard to detect
2014166678.649000e+011666.2502025-08-31 08:00:00Adam Smith is the father of economics
2015250008.043570e+021899.6252025-09-12 12:00:00once upon a time
2016333337.480520e+032133.0002025-09-24 16:00:00risk is hard to define
2017416676.956884e+042366.3752025-10-06 20:00:00not in Kansas anymore
2018500006.469902e+052599.7502025-10-19 00:00:00neutrinos are hard to detect
2019583336.017009e+062833.1252025-10-31 04:00:00Adam Smith is the father of economics
2020666675.595818e+073066.5002025-11-12 08:00:00once upon a time
2021750005.204111e+083299.8752025-11-24 12:00:00risk is hard to define
2022833334.839823e+093533.2502025-12-06 16:00:00not in Kansas anymore
2023916674.501035e+103766.6252025-12-18 20:00:00neutrinos are hard to detect
20241000004.185963e+114000.0002025-12-31 00:00:00Adam Smith is the father of economics
-
-
-
-
-
-
-

Table 1 shows the default output and Table 2 the sGT format output.

-
-
-Code -
sGT(hard, 'A table with varied columns.')
-
-
-
-
-Table 2: Greater Tables output (Quarto generated caption) -
-
-
-
- - - -------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
A table with varied columns.
ABC
years!IntFloatFloat3Longer Text
2000-100,000 2.389p-1,601.002025-03-14once upon a time
2001-91,667 22.217p-1,367.622025-03-26 risk is hard to define
2002-83,333 206.619p-1,134.252025-04-07 not in Kansas anymore
2003-75,000 1.922n-900.882025-04-19 neutrinos are hard to detect
2004-66,667 17.870n-667.502025-05-01 Adam Smith is the father of economics
2005-58,333 166.196n-434.122025-05-13once upon a time
2006-50,000 1.546u-200.752025-05-26 risk is hard to define
2007-41,667 14.374u32.622025-06-07 not in Kansas anymore
2008-33,333 133.681u266.002025-06-19 neutrinos are hard to detect
2009-25,000 1.243m499.382025-07-01 Adam Smith is the father of economics
2010-16,667 11.562m732.752025-07-13once upon a time
2011-8,333 107.527m966.122025-07-25 risk is hard to define
20120 1.0001,199.502025-08-07 not in Kansas anymore
20138,333 9.3001,432.882025-08-19 neutrinos are hard to detect
201416,667 86.4901,666.252025-08-31 Adam Smith is the father of economics
201525,000 804.3571,899.622025-09-12once upon a time
201633,333 7.481k2,133.002025-09-24 risk is hard to define
201741,667 69.569k2,366.382025-10-06 not in Kansas anymore
201850,000 646.990k2,599.752025-10-19 neutrinos are hard to detect
201958,333 6.017M2,833.122025-10-31 Adam Smith is the father of economics
202066,667 55.958M3,066.502025-11-12once upon a time
202175,000 520.411M3,299.882025-11-24 risk is hard to define
202283,333 4.840G3,533.252025-12-06 not in Kansas anymore
202391,667 45.010G3,766.622025-12-18 neutrinos are hard to detect
2024100,000 418.596G4,000.002025-12-31 Adam Smith is the father of economics
-
-
-
-
-
-

Here are some alternatives:

- -
-
-Code -
```{python}
-#| label: tbl-hard-rules-3a
-#| tbl-cap: No V rules but hrules (Quarto generated caption)
-display(sGT(hard.sample(5).sort_index(),
-        caption='GT caption No v rules, but h rules',
-        vrule_widths=(0,0,0),
-        hrule_widths=(1,0,0)))
-```
-
-
-
-
-Table 3: No V rules but hrules (Quarto generated caption) -
-
-
-
- - - -------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
GT caption No v rules, but h rules
ABC
years!IntFloatFloat3Longer Text
2002-83,333 206.619p-1,134.252025-04-07 not in Kansas anymore
2004-66,667 17.870n-667.502025-05-01 Adam Smith is the father of economics
201525,000 804.3571,899.622025-09-12once upon a time
201850,000 646.990k2,599.752025-10-19 neutrinos are hard to detect
202175,000 520.411M3,299.882025-11-24 risk is hard to define
-
-
-
-
-
-
-
-Code -
```{python}
-#| label: tbl-hard-rules-3b
-#| tbl-cap: Change date and integer formats  (Quarto generated caption)
-display(sGT(hard.sample(5).sort_index(),
-        caption='Change default date and integer formats',
-        default_date_str='%m-%d', default_integer_str='[{x:d}]'))
-```
-
-
-
-
-Table 4: Change date and integer formats (Quarto generated caption) -
-
-
-
- - - -------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Change default date and integer formats
ABC
years!IntFloatFloat3Longer Text
2003[-75000] 1.922n-900.8804-19 neutrinos are hard to detect
2005[-58333] 166.196n-434.1205-13once upon a time
2011[-8333] 107.527m966.1207-25 risk is hard to define
2018[50000] 646.990k2,599.7510-19 neutrinos are hard to detect
2023[91667] 45.010G3,766.6212-18 neutrinos are hard to detect
-
-
-
-
-
-
-
-Code -
```{python}
-#| label: tbl-hard-rules-3c
-#| tbl-cap: Change padding and debug mode, boxes (Quarto generated caption)
-display(sGT(hard.sample(5).sort_index(),
-        caption='Change padding, debug mode lines',
-        padding_trbl=(10, 10, 20, 20), debug=True))
-```
-
-
-
-
-Table 5: Change padding and debug mode, boxes (Quarto generated caption) -
-
-
-
- - - -------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Change padding, debug mode lines (id: TEEUJQBUI2GUC)
ABC
years!IntFloatFloat3Longer Text
2004-66,667 17.870n-667.502025-05-01 Adam Smith is the father of economics
2006-50,000 1.546u-200.752025-05-26 risk is hard to define
2008-33,333 133.681u266.002025-06-19 neutrinos are hard to detect
202175,000 520.411M3,299.882025-11-24 risk is hard to define
202283,333 4.840G3,533.252025-12-06 not in Kansas anymore
-
-
-
-
-
-

Here is the raw HTML and LaTeX output.

-
-
-Code -
f = sGT(hard.head(4), debug=True)
-print('HTML output\n')
-print(f._repr_html_())
-
-print('\n\n\nTeX output\n')
-print(f._repr_latex_())
-
-
-
HTML output
-
-<div class="greater-table">
-<style>
-    #TIPUZXJD7G5EM  {
-    border-collapse: collapse;
-    font-family: "Roboto", "Open Sans Condensed", "Arial", 'Segoe UI', sans-serif;
-    font-size: 0.9em;
-    width: auto;
-    /* tb and lr 
-    width: fit-content; */
-    margin: 10px auto; 
-    border: none;
-    overflow: auto;
-    margin-left: auto;
-    margin-right: auto;
-    }
-    /* tag formats */
-    #TIPUZXJD7G5EM caption {
-        padding: 8px 10px 4px 10px;
-        font-size: 0.99em;
-        text-align: center;
-        font-weight: normal;
-        caption-side: top;
-    }
-    #TIPUZXJD7G5EM thead {
-        /* top and bottom of header */
-        border-top: 1px solid #0ff;
-        border-bottom: 1px solid #0ff;
-        font-size: 0.99em;
-        }
-    #TIPUZXJD7G5EM tbody {
-        /* bottom of body */
-        border-bottom: 1px solid #f0f;
-        }
-    #TIPUZXJD7G5EM th  {
-        vertical-align: bottom;
-        padding: 8px 10px 8px 10px;
-    }
-    #TIPUZXJD7G5EM td {
-        /* top, right, bottom left cell padding */
-        padding: 4px 10px 4px 10px;
-        vertical-align: top;
-    }
-    /* class overrides */
-    #TIPUZXJD7G5EM .grt-hrule-0 {
-        border-top: 0px solid #f00;
-    }
-    #TIPUZXJD7G5EM .grt-hrule-1 {
-        border-top: 0px solid #b00;
-    }
-    #TIPUZXJD7G5EM .grt-hrule-2 {
-        border-top: 0px solid #900;
-    }
-    /* for the header, there if you have v lines you want h lines
-       hence use vrule_widths */
-    #TIPUZXJD7G5EM .grt-bhrule-0 {
-        border-bottom: 1.5px solid #f00;
-    }
-    #TIPUZXJD7G5EM .grt-bhrule-1 {
-        border-bottom: 1px solid #b00;
-    }
-    #TIPUZXJD7G5EM .grt-vrule-index {
-        border-left: 1.5px solid #0f0;
-    }
-    #TIPUZXJD7G5EM .grt-vrule-0 {
-        border-left: 1.5px solid #0f0;
-    }
-    #TIPUZXJD7G5EM .grt-vrule-1 {
-        border-left: 1px solid #0a0;
-    }
-    #TIPUZXJD7G5EM .grt-vrule-2 {
-        border-left: 0.5px solid #090;
-    }
-    #TIPUZXJD7G5EM .grt-left {
-        text-align: left;
-    }
-    #TIPUZXJD7G5EM .grt-center {
-        text-align: center;
-    }
-    #TIPUZXJD7G5EM .grt-right {
-        text-align: right;
-        font-variant-numeric: tabular-nums;
-    }
-    #TIPUZXJD7G5EM .grt-head {
-        font-family: "Times New Roman", 'Courier New';
-        font-size: 0.99em;
-    }
-    #TIPUZXJD7G5EM .grt-bold {
-        font-weight: bold;
-    }
-</style>
-<table id="TIPUZXJD7G5EM">
-<caption> (id: TIPUZXJD7G5EM)</caption>
-<colgroup>
-<col style="width: 3.0em;"/>
-<col style="width: 4.0em;"/>
-<col style="width: 4.5em;"/>
-<col style="width: 4.5em;"/>
-<col style="width: 5.0em;"/>
-<col style="width: 14.5em;"/>
-</colgroup>
-<thead>
-<tr>
-<th class="grt-left"></th>
-<th class="grt-center grt-bhrule-0 grt-vrule-index" colspan="2">A</th>
-<th class="grt-center grt-bhrule-0 grt-vrule-0" colspan="2">B</th>
-<th class="grt-center grt-bhrule-0 grt-vrule-0" colspan="1">C</th>
-</tr>
-<tr>
-<th class="grt-left">years!</th>
-<th class="grt-center grt-vrule-index" colspan="1">Int</th>
-<th class="grt-center grt-vrule-1" colspan="1">Float</th>
-<th class="grt-center grt-vrule-0" colspan="1">Float</th>
-<th class="grt-center grt-vrule-1" colspan="1">3</th>
-<th class="grt-center grt-vrule-0" colspan="1">Longer Text</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td class="grt-left">2000</td>
-<td class="grt-right grt-vrule-index">-100,000</td>
-<td class="grt-right grt-vrule-1"> 2.389p</td>
-<td class="grt-right grt-vrule-0">-1,601.00</td>
-<td class="grt-center grt-vrule-1">2025-03-14</td>
-<td class="grt-left grt-vrule-0">once upon a time</td>
-</tr>
-<tr>
-<td class="grt-left grt-hrule-0">2001</td>
-<td class="grt-right grt-hrule-0 grt-vrule-index">-91,667</td>
-<td class="grt-right grt-hrule-0 grt-vrule-1"> 22.217p</td>
-<td class="grt-right grt-hrule-0 grt-vrule-0">-1,367.62</td>
-<td class="grt-center grt-hrule-0 grt-vrule-1">2025-03-26</td>
-<td class="grt-left grt-hrule-0 grt-vrule-0"> risk is hard to define</td>
-</tr>
-<tr>
-<td class="grt-left grt-hrule-0">2002</td>
-<td class="grt-right grt-hrule-0 grt-vrule-index">-83,333</td>
-<td class="grt-right grt-hrule-0 grt-vrule-1"> 206.619p</td>
-<td class="grt-right grt-hrule-0 grt-vrule-0">-1,134.25</td>
-<td class="grt-center grt-hrule-0 grt-vrule-1">2025-04-07</td>
-<td class="grt-left grt-hrule-0 grt-vrule-0"> not in Kansas anymore</td>
-</tr>
-<tr>
-<td class="grt-left grt-hrule-0">2003</td>
-<td class="grt-right grt-hrule-0 grt-vrule-index">-75,000</td>
-<td class="grt-right grt-hrule-0 grt-vrule-1"> 1.922n</td>
-<td class="grt-right grt-hrule-0 grt-vrule-0">-900.88</td>
-<td class="grt-center grt-hrule-0 grt-vrule-1">2025-04-19</td>
-<td class="grt-left grt-hrule-0 grt-vrule-0"> neutrinos are hard to detect</td>
-</tr>
-</tbody>
-</table></div>
-
-
-
-TeX output
-
-
-\begin{tikzpicture}[
-    auto,
-    transform shape,
-    nosep/.style={inner sep=0},
-    table/.style={
-        matrix of nodes,
-        row sep=0.125em,
-        column sep=0.375em,
-        nodes in empty cells,
-        nodes={rectangle, scale=0.635, text badly ragged , draw=blue!10},
-    row 1/.style={nodes={text=black, anchor=north, inner ysep=0, text height=0, text depth=0}},
-    row 2/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}},
-    row 3/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}},
-    column  1/.style={nodes={align=left  }, text height=0.9em, text depth=0.2em, inner xsep=0.375em, inner ysep=0, text width=3.60em},
-    column  2/.style={nodes={align=right }, nosep, text width=17.40em},
-    column  3/.style={nodes={align=right }, nosep, text width=17.40em},
-    column  4/.style={nodes={align=right }, nosep, text width=17.40em},
-    column  5/.style={nodes={align=center}, nosep, text width=17.40em},
-    column  6/.style={nodes={align=left  }, nosep, text width=17.40em},
-    column  7/.style={text height=0.9em, text depth=0.2em, nosep, text width=0em}   }]
-\matrix (TIPUZXJD7G5EM) [table, ampersand replacement=\&]{
-      \&          \&           \&           \&            \&                               \& \\
- \grtspacer \& A\grtspacer \& \grtspacer \& B\grtspacer \& \grtspacer \& C\grtspacer                   \& \\
- years!\grtspacer \& Int\grtspacer \& Float\grtspacer \& Float\grtspacer \& 3\grtspacer \& Longer Text\grtspacer         \& \\
- 2000 \& -100,000 \&    2.389p \& -1,601.00 \& 2025-03-14 \& once upon a time              \& \\
- 2001 \&  -91,667 \&   22.217p \& -1,367.62 \& 2025-03-26 \&  risk is hard to define       \& \\
- 2002 \&  -83,333 \&  206.619p \& -1,134.25 \& 2025-04-07 \&  not in Kansas anymore        \& \\
- 2003 \&  -75,000 \&    1.922n \&   -900.88 \& 2025-04-19 \&  neutrinos are hard to detect \& \\
-};
-
-\path[draw, thick] (TIPUZXJD7G5EM-1-1.south west)  -- (TIPUZXJD7G5EM-1-7.south east);
-\path[draw, semithick] ([yshift=-0.0625em]TIPUZXJD7G5EM-3-1.south west)  -- ([yshift=-0.0625em]TIPUZXJD7G5EM-3-7.south east);
-\path[draw, thick] ([yshift=-0.3125em]TIPUZXJD7G5EM-7-1.base west)  -- ([yshift=-0.3125em]TIPUZXJD7G5EM-7-7.base east);
-\path[draw, very thin] ([xshift=-0.1875em, yshift=-0.0625em]TIPUZXJD7G5EM-2-2.south west)  -- ([yshift=-0.0625em]TIPUZXJD7G5EM-2-7.south east);
-\path[draw, very thin] ([xshift=-0.1875em]TIPUZXJD7G5EM-1-2.south west)  -- ([yshift=-0.3125em, xshift=-0.1875em]TIPUZXJD7G5EM-7-2.base west);
-\path[draw, ultra thin] ([xshift=0.1875em, yshift=-0.0625em]TIPUZXJD7G5EM-1-3.south east)  -- ([yshift=-0.3125em, xshift=0.1875em]TIPUZXJD7G5EM-7-3.base east);
-\path[draw, ultra thin] ([xshift=0.1875em, yshift=-0.0625em]TIPUZXJD7G5EM-1-5.south east)  -- ([yshift=-0.3125em, xshift=0.1875em]TIPUZXJD7G5EM-7-5.base east);
-
-
-
-\end{tikzpicture}
-
-
-
-
-
-

2 A Table with TeX Content

-
-
-Code -
index = pd.Index(["A", "B", "$C_1$", "C_2 not tex", '$\\cos(A)$'])
-tex = pd.DataFrame(
-{'x': np.arange(2020, 2025, dtype=int),
-'b': np.random.random(5),
-'a1': [f'$x^{i}$' for i in range(5,10)],
-'a2': [f'$\\sin({i}x\\pi/n)$' for i in range(5,10)],
-'a3': [f'$x^{i}$' for i in range(5,10)],
-'a4': [f'\\(x^{i}\\)' for i in range(5,10)],
-}).set_index('x')
-tex = tex.head()
-tex.columns = index
-tex
-
-
-
-
-Table 6: (Quarto generated caption): table displayed by default routine. -
-
-
-
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
AB$C_1$C_2 not tex$\cos(A)$
x
20200.718196$x^5$$\sin(5x\pi/n)$$x^5$\(x^5\)
20210.287288$x^6$$\sin(6x\pi/n)$$x^6$\(x^6\)
20220.591513$x^7$$\sin(7x\pi/n)$$x^7$\(x^7\)
20230.697237$x^8$$\sin(8x\pi/n)$$x^8$\(x^8\)
20240.774233$x^9$$\sin(9x\pi/n)$$x^9$\(x^9\)
-
-
-
-
-
-
-
-
-Code -
sGT(tex, 'GT Caption')
-
-
-
-
-Table 7: GT output (Quarto generated caption) -
-
-
-
- - - -------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
GT Caption
xAB\(C_1\)C_2 not tex\(\cos(A)\)
20200.71820\(x^5\)\(\sin(5x\pi/n)\)\(x^5\)\(x^5\)
20210.28729\(x^6\)\(\sin(6x\pi/n)\)\(x^6\)\(x^6\)
20220.59151\(x^7\)\(\sin(7x\pi/n)\)\(x^7\)\(x^7\)
20230.69724\(x^8\)\(\sin(8x\pi/n)\)\(x^8\)\(x^8\)
20240.77423\(x^9\)\(\sin(9x\pi/n)\)\(x^9\)\(x^9\)
-
-
-
-
-
-

Ratio columns.

-
-
-Code -
tex.columns = ["A (%)", "B", "$C_1$", "C_2 not tex", '$\\cos(A)$']
-sGT(tex, 'Ratio columns in A', ratio_cols='A (%)')
-
-
-
-
-Table 8: greater table output -
-
-
-
- - - -------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Ratio columns in A
xA (%)B\(C_1\)C_2 not tex\(\cos(A)\)
202071.8%\(x^5\)\(\sin(5x\pi/n)\)\(x^5\)\(x^5\)
202128.7%\(x^6\)\(\sin(6x\pi/n)\)\(x^6\)\(x^6\)
202259.2%\(x^7\)\(\sin(7x\pi/n)\)\(x^7\)\(x^7\)
202369.7%\(x^8\)\(\sin(8x\pi/n)\)\(x^8\)\(x^8\)
202477.4%\(x^9\)\(\sin(9x\pi/n)\)\(x^9\)\(x^9\)
-
-
-
-
-
-
-
-

3 Greater_tables Test Suite

-
-
-Code -
test_gen = gtu.TestDFGenerator(0, 0)
-ans = test_gen.test_suite()
-
-
-
-

3.1 Test Table: basic

-
-
-Code -
hrw = (0, 0, 0)
-sGT(ans['basic'], "Basic", ratio_cols='z', aligners={'w': 'l'},
-        hrule_widths=hrw)
-
-
-
-
-Table 9: GT output for test table basic -
-
-
-
- - - ----------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Basic
finallydebug dateenemy floatorphans floatprotruding floatprudent datetimeshale intslowness intsuing int
7,8542030-06-262.11142 12.589k 446.533k2030-10-26-2,4209,789-8,700
16,1962007-03-200.00302 5.064 18.008M2018-07-081,0857931,370
17,9252029-07-200.00003 27.621k 396.221M2027-09-17-5,360-4,847-1,221
45,0072025-06-050.02476 7.990M 24.956M2030-10-26-3,2476224,761
46,5972010-11-110.00000 338.592M 182.695M2020-06-219,321-2,5199,025
65,8752009-12-150.00029 7.152G 35.381M2030-10-262,489-8,288-3,648
73,8362025-06-050.00000 290.625k 1.063M2022-02-01-312-9,0068,417
79,3242016-02-070.00001 966.832k 109.231M2030-08-264,735-5,085-9,105
88,0492016-10-200.00000 4.929G 31.366k2024-06-27-5,858-1,554-5,719
89,9512010-11-110.00000 6.406G 46.693M2024-06-27-7,4446,314-2,130
-
-
-
-
-
-

Comments go here.

-
-
-

3.2 Test Table: timeseries

-
-
-Code -
hrw = (0, 0, 0)
-sGT(ans['timeseries'], "Timeseries", ratio_cols='z', aligners={'w': 'l'},
-        hrule_widths=hrw)
-
-
-
-
-Table 10: GT output for test table timeseries -
-
-
-
- - - ------ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Timeseries
hourAghast Forth Recast floatBorderline Comprehension Quicksand floatReads Touch Cluck date
2006-06-140.00063 5.086M2016-01-16
2008-01-220.00189 135.050k2018-06-16
2011-07-240.00006 674.425k2026-01-30
2014-02-200.00025 32.0132026-01-30
2015-07-220.00000 2.034k2026-01-30
2017-03-130.87787 291.515k2029-11-24
2017-05-280.00340 14.176k2019-08-15
2017-09-020.01595 4.440k2026-01-30
2018-06-300.00000 877.971m2012-05-30
2018-10-090.43277 2.863G2022-08-10
2019-06-180.00203 77.727M2020-10-20
2019-06-270.00051 22.6722007-01-02
2020-04-140.00000 118.617k2016-01-16
2025-03-130.02163 167.999m2019-08-15
2027-10-010.06213 4.3502007-01-02
2027-11-090.00000 169.9602020-10-20
2029-02-140.00000 376.827k2019-08-15
2031-01-040.00030 1.146k2025-05-23
2031-04-210.00000 3.568k2025-02-09
2033-06-100.04446 63.823k2012-05-30
-
-
-
-
-
-

Comments go here.

-
-
-

3.3 Test Table: multiindex

-
-
-Code -
hrw = (1.5, 1.0, 0.5)
-sGT(ans['multiindex'], "Multiindex", ratio_cols='z', aligners={'w': 'l'},
-        hrule_widths=hrw)
-
-
-
-
-Table 11: GT output for test table multiindex -
-
-
-
- - - ---------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Multiindex
subcontractorsomniscientdopeClutch Potent Proxies intColoration Brains Trimester datetimeHomicide Mangrove Medicaid floatMulled Mall Overturned floatViability Cannon Reaffirmed int
41,778nurtured4,716737,371,2462006-07-28 318.230n0.000005,631
11,541628,029,5632028-05-19 115.862n0.00242-2,675
39,040952,951,4402030-08-28 4.728u0.00000-8,399
operational85,483406,112,4202030-08-28 12.120n0.00000-5,313
99,029250,843,9072030-08-28 2.035n0.00310-8,481
91,316nurtured11,58383,924,6622030-08-28 51.575n0.000004,604
15,228164,891,4082007-03-31 1.860m0.000009,813
93,958558,988,2292009-11-18 1.924n0.03481-4,138
operational11,208395,204,1912021-06-25 1.513m0.226962,835
scratches14,298579,583,0912030-08-28 2.781u0.00002-2,621
-
-
-
-
-
-

Comments go here.

-
-
-

3.4 Test Table: multicolumns

-
-
-Code -
hrw = (0, 0, 0)
-sGT(ans['multicolumns'], "Multicolumns", ratio_cols='z', aligners={'w': 'l'},
-        hrule_widths=hrw)
-
-
-
-
-Table 12: GT output for test table multicolumns -
-
-
-
- - - -------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Multicolumns
guiltyspying
shadowsmonitoredrevelshadows
influenzacommentingredirectedvowelsdebuggingexplode
16,750utilizes2019-01-030.00000 93.987k2024-02-20
34,377thoroughness2013-01-150.00023 3.075M2010-05-22
44,533uprisings2029-11-290.00000 38.750k2016-05-25
54,472critter2014-06-250.00038 9.971k2031-10-04
64,171destiny2029-11-290.09353 1.720G2030-03-12
71,922savvy2025-04-200.00000 5.788k2010-05-22
79,803alright2013-01-150.00001 356.950M2031-10-04
87,194solidifies2013-08-010.00009 1.301k2030-12-05
90,818acquires2014-06-250.00000 32.7882031-10-31
94,143fines2014-06-250.13375 5.0772031-10-04
-
-
-
-
-
-

Comments go here.

-
-
-

3.5 Test Table: complex

-
-
-Code -
hrw = (1.5, 1.0, 0.5)
-sGT(ans['complex'], "Complex", ratio_cols='z', aligners={'w': 'l'},
-        hrule_widths=hrw)
-
-
-
-
-Table 13: GT output for test table complex -
-
-
-
- - - --------------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Complex
partitioningperturbed
criedrecoilsaddenedcriedrecoilsaddened
ninesrichescreativemercilessquirksunconstraineddesegregationfreezerqueueracetrackradiologicalsubstanceslocked
51,924inventions10,331 2.623M0.0000020132016-950.847p 18.245k 183.787M19970.263462020-03-08
27,378 5.630G0.5687220272005-8.399m 14.163M 3.408k20190.000012021-10-05
33,898 780.044M0.6414519952007 434.460k 6.827k 50.624k20240.633192030-01-16
92,471 40.028k0.0000819982021-0.103y 30.670 39.138M20030.000002008-02-13
nuclear9,425 81.988M0.0000020022000-277.700Z 7.089 159.617M20271.235742015-03-08
14,347 24.193k0.0122520262022-64.380n 136.721k 107.42419990.000372015-03-08
62,320 2.147M0.0000020162028 40.642M 292.944 1.390G20080.000002030-07-09
repudiate79,676 1.807G0.0000020222005 3.843Z 12.544k 1.814k19970.000002008-02-13
54,240inventions10,825 356.1560.3705920022024-8.059Z 369.243m 264.911k20090.001972022-12-26
21,803 210.0240.1957320162011 1066900.627Y 22.193k 4.962G19930.000002012-03-17
96,698 7.274G0.0004620201995-2.932a 1.422k 853.603M20210.004532015-08-06
nuclear47,064 3.393G0.0247019962003-0.000y 26.800 371.147k20030.000002020-03-08
82,929 23.3450.0016220042017-337.974P 1.629G 63.656M20290.000092030-07-09
repudiate27,297 152.8240.0203719982013 11177879989333.562Y 64.290k 12.063M20090.000002021-10-05
38,293 60.465M3.2434520022017 4.351Y 781.098M 2.66420040.000002015-08-06
43,065 203.4280.0045920222028-47.829P 1.409M 473.835M19950.002152020-03-08
53,192 131.6110.0000019952003 9.008P 3.915G 10.812M20240.000562026-05-02
56,629 9.537G0.0084219941994-0.000y 6.550k 805.653k20060.034492011-01-10
69,244 1.7870.0000020102007 3.397 267.352M 3.369M20260.000012020-03-08
82,911 30.563k0.0000220212017-0.000y 30.860k 42.57020260.000002029-07-23
-
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Comments go here.

-
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4 Other input formats

-
-

4.1 Markown

- ------ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Insured group or insurance productSatRPRF
Non-standard autox
General liability for judgment proof corporationx
Term life insurancex
Catastrophe Reinsurance, outside rating agency boundsx
High limit property per risk reinsurancex
Personal lines for affluent individualsxx
Small commercial linesxx
Catastrophe reinsurance, within rating agency boundsxx
Large account captive reinsurancex
Structured quota share, requiring a risk transfer testxx
Working layer casualty excess of lossxx
Surplus relief quota share on cat exposed linexxx
Middle market commercial lines work comp or commercial autoxxx
-
-
-Code -
txt = '''
-
-| **Insured group or insurance product**                      | **Sat** | **RP** | **RF** |
-|:------------------------------------------------------------|:-------:|:------:|:------:|
-| Non-standard auto                                           |    x    |        |        |
-| General liability for judgment proof corporation            |    x    |        |        |
-| Term life insurance                                         |         |   x    |        |
-| Catastrophe Reinsurance, outside rating agency bounds       |         |   x    |        |
-| High limit property per risk reinsurance                    |         |   x    |        |
-| Personal lines for affluent individuals                     |    x    |   x    |        |
-| Small commercial lines                                      |    x    |   x    |        |
-| Catastrophe reinsurance, within rating agency bounds        |    x    |   x    |        |
-| Large account captive reinsurance                           |         |        |   x    |
-| Structured quota share, requiring a risk transfer test      |    x    |        |   x    |
-| Working layer casualty excess of loss                       |         |   x    |   x    |
-| Surplus relief quota share on cat exposed line              |    x    |   x    |   x    |
-| Middle market commercial lines work comp or commercial auto |    x    |   x    |   x    |
-
-
-'''
-
-GT(txt)
-
-
-
-
-Table 14: GT from markdown table input -
-
-
-
- - ------ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Insured group or insurance productSatRPRF
Non-standard autox
General liability for judgment proof corporationx
Term life insurancex
Catastrophe Reinsurance, outside rating agency boundsx
High limit property per risk reinsurancex
Personal lines for affluent individualsxx
Small commercial linesxx
Catastrophe reinsurance, within rating agency boundsxx
Large account captive reinsurancex
Structured quota share, requiring a risk transfer testxx
Working layer casualty excess of lossxx
Surplus relief quota share on cat exposed linexxx
Middle market commercial lines work comp or commercial autoxxx
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4.2 List of lists

-
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-Code -
lol = [['a', 'b', 'c', 'd'], ['west', 10, 20, 30], ['east', 10, 200, 30], ['north', 10, 20, 300], ['south', 100, 20, 30]]
-GT(lol)
-
-
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-Table 15: GT output for list of lists input -
-
-
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- - ------ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
abcd
west102030
east1020030
north1020300
south1002030
-
-
-
-
-
- -
-
- -
- - -
- - - - - - \ No newline at end of file diff --git a/tests/tables.ipynb b/tests/tables.ipynb deleted file mode 100644 index d8ea082..0000000 --- a/tests/tables.ipynb +++ /dev/null @@ -1,5244 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "---\n", - "title: All Tables Test - New TestDFGenerator test_suite\n", - "author:\n", - " - name: Stephen J. Mildenhall\n", - " orcid: 0000-0001-6956-0098\n", - " corresponding: true\n", - " email: mynl@me.com\n", - "date: last-modified\n", - "colorlinks: true\n", - "link-citations: true\n", - "link-bibliography: true\n", - "tbl-align: left\n", - "number-sections: true\n", - "number-offset: 0\n", - "number-depth: 3\n", - "code-line-numbers: false\n", - "code-copy: true\n", - "code-overflow: wrap\n", - "code-fold: true\n", - "fig-format: svg\n", - "fig-align: left\n", - "format:\n", - " html:\n", - " html-table-processing: none\n", - " theme: litera\n", - " fontsize: 0.9em\n", - " css: styles.css\n", - " include-in-header: pmir-header.html\n", - " smooth-scroll: true\n", - " toc-title: 'In this chapter:'\n", - " citations-hover: true\n", - " crossrefs-hover: false\n", - " fig-responsive: true\n", - " footnotes-hover: true\n", - " lightbox: true\n", - " link-external-icon: true\n", - " link-external-newwindow: true\n", - " page-layout: article\n", - " page-navigation: true\n", - " reference-section-title: ' '\n", - " page-footer:\n", - " left: 'Stephen J. Mildenhall. License: [CC BY-SA 2.0](https://creativecommons.org/licenses/by-sa/2.0/).'\n", - " twitter-card: true\n", - " open-graph: true\n", - " toc: true\n", - " toc-depth: 3\n", - " math: mathjax\n", - " pdf:\n", - " include-in-header: prefobnicate.tex\n", - " documentclass: scrartcl\n", - " papersize: a4\n", - " fontsize: 11pt\n", - " keep-tex: true\n", - " geometry: margin=0.8in\n", - " pdf-engine: lualatex\n", - " pdf-engine-opts:\n", - " - '-interaction=nonstopmode'\n", - " toc: false\n", - "execute:\n", - " eval: true\n", - " echo: true\n", - " cache: true\n", - " cache-type: jupyter\n", - " freeze: false\n", - " kernel: python3\n", - " engine: jupyter\n", - " daemon: 1200\n", - "jupyter:\n", - " jupytext:\n", - " formats: ipynb,qmd:quarto\n", - " text_representation:\n", - " extension: .qmd\n", - " format_name: quarto\n", - " format_version: '1.0'\n", - " jupytext_version: 1.16.4\n", - " kernelspec:\n", - " display_name: Python 3 (ipykernel)\n", - " language: python\n", - " name: python3\n", - "---" - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "metadata": {}, - "outputs": [], - "source": [ - "#| echo: true\n", - "#| label: setup\n", - "from IPython.display import HTML, display\n", - "import matplotlib as mpl\n", - "import matplotlib.dates as mdates\n", - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "import pandas as pd\n", - "\n", - "import greater_tables as gter\n", - "import greater_tables.utilities as gtu\n", - "from greater_tables import GT, sGT\n", - "gter.logger.setLevel(gter.logging.WARNING)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "...code build completed. \n", - "\n", - "# A Hard-Rules table\n", - "\n", - "Second level index has mixed types. Range of magnitudes. Picking out years.\n", - "\n", - "\\footnotesize" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": 61, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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Level 1ABC
Level 2IntFloatFloat3Longer Text
years!
2000-1000002.388937e-12-1601.0002025-03-14 00:00:00once upon a time
2001-916672.221711e-11-1367.6252025-03-26 04:00:00risk is hard to define
2002-833332.066191e-10-1134.2502025-04-07 08:00:00not in Kansas anymore
2003-750001.921558e-09-900.8752025-04-19 12:00:00neutrinos are hard to detect
2004-666671.787049e-08-667.5002025-05-01 16:00:00Adam Smith is the father of economics
2005-583331.661955e-07-434.1252025-05-13 20:00:00once upon a time
2006-500001.545619e-06-200.7502025-05-26 00:00:00risk is hard to define
2007-416671.437425e-0532.6252025-06-07 04:00:00not in Kansas anymore
2008-333331.336805e-04266.0002025-06-19 08:00:00neutrinos are hard to detect
2009-250001.243229e-03499.3752025-07-01 12:00:00Adam Smith is the father of economics
2010-166671.156203e-02732.7502025-07-13 16:00:00once upon a time
2011-83331.075269e-01966.1252025-07-25 20:00:00risk is hard to define
201201.000000e+001199.5002025-08-07 00:00:00not in Kansas anymore
201383339.300000e+001432.8752025-08-19 04:00:00neutrinos are hard to detect
2014166678.649000e+011666.2502025-08-31 08:00:00Adam Smith is the father of economics
2015250008.043570e+021899.6252025-09-12 12:00:00once upon a time
2016333337.480520e+032133.0002025-09-24 16:00:00risk is hard to define
2017416676.956884e+042366.3752025-10-06 20:00:00not in Kansas anymore
2018500006.469902e+052599.7502025-10-19 00:00:00neutrinos are hard to detect
2019583336.017009e+062833.1252025-10-31 04:00:00Adam Smith is the father of economics
2020666675.595818e+073066.5002025-11-12 08:00:00once upon a time
2021750005.204111e+083299.8752025-11-24 12:00:00risk is hard to define
2022833334.839823e+093533.2502025-12-06 16:00:00not in Kansas anymore
2023916674.501035e+103766.6252025-12-18 20:00:00neutrinos are hard to detect
20241000004.185963e+114000.0002025-12-31 00:00:00Adam Smith is the father of economics
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A table with varied columns.
ABC
years!IntFloatFloat3Longer Text
2000-100,000 2.389p-1,601.002025-03-14once upon a time
2001-91,667 22.217p-1,367.622025-03-26 risk is hard to define
2002-83,333 206.619p-1,134.252025-04-07 not in Kansas anymore
2003-75,000 1.922n-900.882025-04-19 neutrinos are hard to detect
2004-66,667 17.870n-667.502025-05-01 Adam Smith is the father of economics
2005-58,333 166.196n-434.122025-05-13once upon a time
2006-50,000 1.546u-200.752025-05-26 risk is hard to define
2007-41,667 14.374u32.622025-06-07 not in Kansas anymore
2008-33,333 133.681u266.002025-06-19 neutrinos are hard to detect
2009-25,000 1.243m499.382025-07-01 Adam Smith is the father of economics
2010-16,667 11.562m732.752025-07-13once upon a time
2011-8,333 107.527m966.122025-07-25 risk is hard to define
20120 1.0001,199.502025-08-07 not in Kansas anymore
20138,333 9.3001,432.882025-08-19 neutrinos are hard to detect
201416,667 86.4901,666.252025-08-31 Adam Smith is the father of economics
201525,000 804.3571,899.622025-09-12once upon a time
201633,333 7.481k2,133.002025-09-24 risk is hard to define
201741,667 69.569k2,366.382025-10-06 not in Kansas anymore
201850,000 646.990k2,599.752025-10-19 neutrinos are hard to detect
201958,333 6.017M2,833.122025-10-31 Adam Smith is the father of economics
202066,667 55.958M3,066.502025-11-12once upon a time
202175,000 520.411M3,299.882025-11-24 risk is hard to define
202283,333 4.840G3,533.252025-12-06 not in Kansas anymore
202391,667 45.010G3,766.622025-12-18 neutrinos are hard to detect
2024100,000 418.596G4,000.002025-12-31 Adam Smith is the father of economics
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" 2014 \\& 16,667 \\& 86.490 \\& 1,666.25 \\& 2025-08-31 \\& Adam Smith is the father of economics \\& \\\\\n", - " 2015 \\& 25,000 \\& 804.357 \\& 1,899.62 \\& 2025-09-12 \\& once upon a time \\& \\\\\n", - " 2016 \\& 33,333 \\& 7.481k \\& 2,133.00 \\& 2025-09-24 \\& risk is hard to define \\& \\\\\n", - " 2017 \\& 41,667 \\& 69.569k \\& 2,366.38 \\& 2025-10-06 \\& not in Kansas anymore \\& \\\\\n", - " 2018 \\& 50,000 \\& 646.990k \\& 2,599.75 \\& 2025-10-19 \\& neutrinos are hard to detect \\& \\\\\n", - " 2019 \\& 58,333 \\& 6.017M \\& 2,833.12 \\& 2025-10-31 \\& Adam Smith is the father of economics \\& \\\\\n", - " 2020 \\& 66,667 \\& 55.958M \\& 3,066.50 \\& 2025-11-12 \\& once upon a time \\& \\\\\n", - " 2021 \\& 75,000 \\& 520.411M \\& 3,299.88 \\& 2025-11-24 \\& risk is hard to define \\& \\\\\n", - " 2022 \\& 83,333 \\& 4.840G \\& 3,533.25 \\& 2025-12-06 \\& not in Kansas anymore \\& \\\\\n", - " 2023 \\& 91,667 \\& 45.010G \\& 3,766.62 \\& 2025-12-18 \\& neutrinos are hard to detect \\& \\\\\n", - 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GT caption No v rules, but h rules
ABC
years!IntFloatFloat3Longer Text
2000-100,0000-1,601.002025-03-14once upon a time
2002-83,3330-1,134.252025-04-07 not in Kansas anymore
2003-75,0000-900.882025-04-19 neutrinos are hard to detect
2008-33,3330266.002025-06-19 neutrinos are hard to detect
201850,000646,9902,599.752025-10-19 neutrinos are hard to detect
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Change default date and integer formats
ABC
years!IntFloatFloat3Longer Text
2001[-91667]0-1,367.6203-26 risk is hard to define
2004[-66667]0-667.5005-01 Adam Smith is the father of economics
2007[-41667]032.6206-07 not in Kansas anymore
2008[-33333]0266.0006-19 neutrinos are hard to detect
2018[50000]646,9902,599.7510-19 neutrinos are hard to detect
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Change padding, debug mode lines (id: TBM2NV7BWZEMG)
ABC
years!IntFloatFloat3Longer Text
2007-41,667 14.374u32.622025-06-07 not in Kansas anymore
2008-33,333 133.681u266.002025-06-19 neutrinos are hard to detect
201416,667 86.4901,666.252025-08-31 Adam Smith is the father of economics
201633,333 7.481k2,133.002025-09-24 risk is hard to define
202175,000 520.411M3,299.882025-11-24 risk is hard to define
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(id: TWRLFJOULVHRG)
ABC
years!IntFloatFloat3Longer Text
2000-100,000 2.389p-1,601.002025-03-14once upon a time
2001-91,667 22.217p-1,367.622025-03-26 risk is hard to define
2002-83,333 206.619p-1,134.252025-04-07 not in Kansas anymore
2003-75,000 1.922n-900.882025-04-19 neutrinos are hard to detect
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AB$C_1$C_2 not tex$\\cos(A)$
x
20200.424657$x^5$$\\sin(5x\\pi/n)$$x^5$\\(x^5\\)
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20240.519346$x^9$$\\sin(9x\\pi/n)$$x^9$\\(x^9\\)
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GT Caption
xAB\\(C_1\\)C_2 not tex\\(\\cos(A)\\)
20200.42466\\(x^5\\)\\(\\sin(5x\\pi/n)\\)\\(x^5\\)\\(x^5\\)
20210.20928\\(x^6\\)\\(\\sin(6x\\pi/n)\\)\\(x^6\\)\\(x^6\\)
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Ratio columns in A
xA (%)B\\(C_1\\)C_2 not tex\\(\\cos(A)\\)
202042.5%\\(x^5\\)\\(\\sin(5x\\pi/n)\\)\\(x^5\\)\\(x^5\\)
202120.9%\\(x^6\\)\\(\\sin(6x\\pi/n)\\)\\(x^6\\)\\(x^6\\)
20226.8%\\(x^7\\)\\(\\sin(7x\\pi/n)\\)\\(x^7\\)\\(x^7\\)
202379.7%\\(x^8\\)\\(\\sin(8x\\pi/n)\\)\\(x^8\\)\\(x^8\\)
202451.9%\\(x^9\\)\\(\\sin(9x\\pi/n)\\)\\(x^9\\)\\(x^9\\)
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Basic
unintentionallyamply floatdeeper strgrains dateindicators datetimeinject intoriginates strphilosophers intsnowy float
8,003 12.899Mmalicious2025-09-082010-07-06-3,452contracts693,336,903 5.120
18,582 858.904manufacturers2023-05-022015-06-127,457collapse789,639,196 765.357m
18,825 229.354kshortfall2030-08-242008-08-21-2,476sprawl741,809,916 8.096k
20,431 5.300plugs2023-03-072019-03-272,255generalize993,293,639 106.115m
61,650 461.180msetter2023-03-072015-06-129,625downright577,547,084 178.442k
65,395 230.601longhorn2033-05-292024-10-10-5,797humor821,555,659 2.267M
69,741 829.476secretly2025-02-102024-09-189,649hills99,644,183 97.579k
74,709 110.246strove2033-05-292008-08-211,255monster128,426,346 404.926k
77,783 7.586conclusive2030-08-242023-04-294,827proffer818,501,173 18.774k
97,969 10.485kjosephine2025-02-102024-09-187,937permissions38,019,258 538.646
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Timeseries
bushesAcquired Bars Renter dateBristle Engagement Backwater datetimeHeighten Boning Unlucky float
2008-07-102012-05-162010-10-14 517.008E
2009-03-252026-04-052020-03-31 0.000y
2009-08-092017-04-252016-04-01-29.269u
2010-02-012026-04-052013-07-14 0.000y
2010-12-312024-01-032016-11-20-30.741u
2014-06-202032-11-162016-04-01 1.250m
2015-02-132026-04-052016-11-20 335.357f
2018-03-192012-05-162029-02-11-102.890Z
2018-12-072024-07-262019-01-14-0.022y
2019-10-292007-07-132013-07-14 1.216k
2021-08-212024-10-122025-07-11 43.521a
2021-11-122007-07-132031-10-24-0.000y
2025-01-012009-04-132016-04-01-631123020.816Y
2026-01-102017-04-252029-02-11 0.000y
2026-12-272017-04-252016-11-20-0.000y
2027-09-202026-04-052016-04-01 3321909909.577Y
2028-12-232014-04-092032-03-29-25.876Z
2029-11-142018-03-162029-02-11-69.776E
2031-04-202007-07-132016-04-01-2.204k
2031-08-192032-11-162019-01-14 32915.427Y
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Multiindex
phantomanimaldirectionBitty Youthful Express floatImmunity Counts Hose datePennies Reveals Afresh dateSpotty Paralleling Discreet dateStanley Quarrel Alligator str
18,496assent43,0860.000032010-04-132033-01-252033-01-12areas
85,7800.360672027-07-102032-01-232025-10-22mantra
crusader63,5350.000002027-07-102029-09-042008-11-09refers
87,8260.000032029-08-312021-11-142010-09-03ministerial
magnetic10,1110.004622022-12-072021-06-142023-01-22woods
14,3500.000002010-04-132022-03-162023-01-22codification
43,7530.011002019-02-172029-09-042009-05-18object
98,6820.000002027-07-102033-01-252009-02-12dusty
51,439assent93,0010.000002031-07-032021-11-142020-10-04lama
crusader49,6880.000002022-12-072021-11-142033-01-12citizen
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Multicolumns
psychicskirted
pressventuredventured
stimulationgallingunopenedpessimismskingeneva
5,3090.00001penalizing20202030-02-110.20600
6,0290.00000guise20092022-03-180.00003
8,0653.27603pseudo20082008-07-275.65328
14,7490.04182instituted20252009-06-050.00034
43,0620.00000redeemable19952029-05-290.00000
61,8720.19522seth20062022-03-180.00000
69,9790.22767aimless20002028-03-060.00000
70,5260.00226affirms19932008-07-270.00035
81,0720.00000spain20222028-03-060.00000
89,0600.00001underemployed20112008-07-270.02550
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Complex
casualtycopenhagen
negatingsimmeringautisticnegatingsimmering
hardingbrokenloosenedbachelordrawingsarbitratedcashingangelsbeneficiarylendingstudiouslyparaplegicunwieldy
49,146brew2930.062952010-05-152031-06-121997chore937,952,7420.000012031-08-060.000002014
3,4261.965862013-08-052029-08-202008race804,609,9670.000002013-10-190.001382015
19,8710.000002028-03-182011-02-161993economy268,719,6180.000012013-10-190.000281994
77,9700.000032028-03-182008-09-292023exes4,595,8444.231082013-10-190.008542015
fastest13,8560.000002008-07-292007-03-021995intrinsically655,235,8020.000092033-05-090.000022004
31,4180.000012031-03-122028-10-192019cradles657,320,7590.000002018-11-170.000002001
35,0220.000002016-08-012010-04-212027massage283,304,1670.000002020-09-020.005492029
80,1080.175482031-03-122017-05-222018puzzled925,082,0700.000002013-10-191.889622021
fliers25,9360.000152016-09-042017-12-132029computations426,967,5830.000002032-04-150.000001999
64,4330.000002016-06-182007-05-292004passages612,446,4710.000172032-04-150.499592009
80,2290.225592016-06-182017-07-052018repeat112,776,8016.776172024-07-090.000002022
86,639brew13,9640.000002016-08-012007-03-022017frills821,529,7830.071682014-09-270.000002025
41,5930.000032008-07-292007-05-292016endorsing806,241,8460.029602027-10-150.000012002
43,8500.000002007-01-122011-02-211991editorially521,714,1100.222572031-08-060.000152024
82,5470.000002016-08-012007-03-022027february971,932,9271.455592015-10-180.000061997
fastest49,9010.000002027-11-122029-08-202022fancier69,371,8251.235702008-10-250.001172009
59,1510.007232018-04-242029-11-192022hope675,380,4080.080462015-10-180.000011992
85,9300.000002015-06-242025-05-142020decried923,139,3670.000002015-10-180.000012009
fliers45,8760.008302018-12-172025-05-142019proximate721,860,8810.000062012-02-230.022562028
74,6670.000002023-08-032028-10-132001cautionary44,092,4540.000012008-10-252.240842027
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" \\grtspacer \\& \\grtspacer \\& \\grtspacer \\& negating\\grtspacer \\& \\grtspacer \\& simmering\\grtspacer \\& \\grtspacer \\& autistic\\grtspacer \\& \\grtspacer \\& negating\\grtspacer \\& \\grtspacer \\& simmering\\grtspacer \\& \\grtspacer \\& \\\\\n", - " harding\\grtspacer \\& broken\\grtspacer \\& loosened\\grtspacer \\& bachelor\\grtspacer \\& drawings\\grtspacer \\& arbitrated\\grtspacer \\& cashing\\grtspacer \\& angels\\grtspacer \\& beneficiary\\grtspacer \\& lending\\grtspacer \\& studiously\\grtspacer \\& paraplegic\\grtspacer \\& unwieldy\\grtspacer \\& \\\\\n", - " 49,146 \\& brew \\& 293 \\& 0.06295 \\& 2010-05-15 \\& 2031-06-12 \\& 1997 \\& chore \\& 937,952,742 \\& 0.00001 \\& 2031-08-06 \\& 0.00000 \\& 2014 \\& \\\\\n", - " \\& brew \\& 3,426 \\& 1.96586 \\& 2013-08-05 \\& 2029-08-20 \\& 2008 \\& race \\& 804,609,967 \\& 0.00000 \\& 2013-10-19 \\& 0.00138 \\& 2015 \\& \\\\\n", - " \\& brew \\& 19,871 \\& 0.00000 \\& 2028-03-18 \\& 2011-02-16 \\& 1993 \\& economy \\& 268,719,618 \\& 0.00001 \\& 2013-10-19 \\& 0.00028 \\& 1994 \\& \\\\\n", - " \\& brew \\& 77,970 \\& 0.00003 \\& 2028-03-18 \\& 2008-09-29 \\& 2023 \\& exes \\& 4,595,844 \\& 4.23108 \\& 2013-10-19 \\& 0.00854 \\& 2015 \\& \\\\\n", - " \\& fastest \\& 13,856 \\& 0.00000 \\& 2008-07-29 \\& 2007-03-02 \\& 1995 \\& intrinsically \\& 655,235,802 \\& 0.00009 \\& 2033-05-09 \\& 0.00002 \\& 2004 \\& \\\\\n", - " \\& fastest \\& 31,418 \\& 0.00001 \\& 2031-03-12 \\& 2028-10-19 \\& 2019 \\& cradles \\& 657,320,759 \\& 0.00000 \\& 2018-11-17 \\& 0.00000 \\& 2001 \\& \\\\\n", - " \\& fastest \\& 35,022 \\& 0.00000 \\& 2016-08-01 \\& 2010-04-21 \\& 2027 \\& massage \\& 283,304,167 \\& 0.00000 \\& 2020-09-02 \\& 0.00549 \\& 2029 \\& \\\\\n", - " \\& fastest \\& 80,108 \\& 0.17548 \\& 2031-03-12 \\& 2017-05-22 \\& 2018 \\& puzzled \\& 925,082,070 \\& 0.00000 \\& 2013-10-19 \\& 1.88962 \\& 2021 \\& \\\\\n", - " \\& fliers \\& 25,936 \\& 0.00015 \\& 2016-09-04 \\& 2017-12-13 \\& 2029 \\& computations \\& 426,967,583 \\& 0.00000 \\& 2032-04-15 \\& 0.00000 \\& 1999 \\& \\\\\n", - " \\& fliers \\& 64,433 \\& 0.00000 \\& 2016-06-18 \\& 2007-05-29 \\& 2004 \\& passages \\& 612,446,471 \\& 0.00017 \\& 2032-04-15 \\& 0.49959 \\& 2009 \\& \\\\\n", - " \\& fliers \\& 80,229 \\& 0.22559 \\& 2016-06-18 \\& 2017-07-05 \\& 2018 \\& repeat \\& 112,776,801 \\& 6.77617 \\& 2024-07-09 \\& 0.00000 \\& 2022 \\& \\\\\n", - " 86,639 \\& brew \\& 13,964 \\& 0.00000 \\& 2016-08-01 \\& 2007-03-02 \\& 2017 \\& frills \\& 821,529,783 \\& 0.07168 \\& 2014-09-27 \\& 0.00000 \\& 2025 \\& \\\\\n", - " \\& brew \\& 41,593 \\& 0.00003 \\& 2008-07-29 \\& 2007-05-29 \\& 2016 \\& endorsing \\& 806,241,846 \\& 0.02960 \\& 2027-10-15 \\& 0.00001 \\& 2002 \\& \\\\\n", - " \\& brew \\& 43,850 \\& 0.00000 \\& 2007-01-12 \\& 2011-02-21 \\& 1991 \\& editorially \\& 521,714,110 \\& 0.22257 \\& 2031-08-06 \\& 0.00015 \\& 2024 \\& \\\\\n", - " \\& brew \\& 82,547 \\& 0.00000 \\& 2016-08-01 \\& 2007-03-02 \\& 2027 \\& february \\& 971,932,927 \\& 1.45559 \\& 2015-10-18 \\& 0.00006 \\& 1997 \\& \\\\\n", - " \\& fastest \\& 49,901 \\& 0.00000 \\& 2027-11-12 \\& 2029-08-20 \\& 2022 \\& fancier \\& 69,371,825 \\& 1.23570 \\& 2008-10-25 \\& 0.00117 \\& 2009 \\& \\\\\n", - " \\& fastest \\& 59,151 \\& 0.00723 \\& 2018-04-24 \\& 2029-11-19 \\& 2022 \\& hope \\& 675,380,408 \\& 0.08046 \\& 2015-10-18 \\& 0.00001 \\& 1992 \\& \\\\\n", - " \\& fastest \\& 85,930 \\& 0.00000 \\& 2015-06-24 \\& 2025-05-14 \\& 2020 \\& decried \\& 923,139,367 \\& 0.00000 \\& 2015-10-18 \\& 0.00001 \\& 2009 \\& \\\\\n", - " \\& fliers \\& 45,876 \\& 0.00830 \\& 2018-12-17 \\& 2025-05-14 \\& 2019 \\& proximate \\& 721,860,881 \\& 0.00006 \\& 2012-02-23 \\& 0.02256 \\& 2028 \\& \\\\\n", - " \\& fliers \\& 74,667 \\& 0.00000 \\& 2023-08-03 \\& 2028-10-13 \\& 2001 \\& cautionary \\& 44,092,454 \\& 0.00001 \\& 2008-10-25 \\& 2.24084 \\& 2027 \\& \\\\\n", - "};\n", - "\n", - "\\path[draw, thick] (TQT25W6I6LKNW-1-1.south west) -- (TQT25W6I6LKNW-1-14.south east);\n", - "\\path[draw, thick] ([yshift=-0.3125em]TQT25W6I6LKNW-24-1.base west) -- ([yshift=-0.3125em]TQT25W6I6LKNW-24-14.base east);\n", - 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"|:------------------------------------------------------------|:-------:|:------:|:------:|\n", - "| Non-standard auto | x | | |\n", - "| General liability for judgment proof corporation | x | | |\n", - "| Term life insurance | | x | |\n", - "| Catastrophe Reinsurance, outside rating agency bounds | | x | |\n", - "| High limit property per risk reinsurance | | x | |\n", - "| Personal lines for affluent individuals | x | x | |\n", - "| Small commercial lines | x | x | |\n", - "| Catastrophe reinsurance, within rating agency bounds | x | x | |\n", - "| Large account captive reinsurance | | | x |\n", - "| Structured quota share, requiring a risk transfer test | x | | x |\n", - "| Working layer casualty excess of loss | | x | x |\n", - "| Surplus relief quota share on cat exposed line | x | x | x |\n", - "| Middle market commercial lines work comp or commercial auto | x | x | x |\n" - ] - }, - { - "cell_type": "code", - "execution_count": 78, - "metadata": {}, - "outputs": [ - { - "data": { - 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Mildenhall - orcid: 0000-0001-6956-0098 - corresponding: true - email: mynl@me.com -date: last-modified -colorlinks: true -link-citations: true -link-bibliography: true -tbl-align: left -number-sections: true -number-offset: 0 -number-depth: 3 -code-line-numbers: false -code-copy: true -code-overflow: wrap -code-fold: true -fig-format: svg -fig-align: left -format: - html: - html-table-processing: none - theme: litera - fontsize: 0.9em - css: styles.css - include-in-header: pmir-header.html - smooth-scroll: true - toc-title: 'In this chapter:' - citations-hover: true - crossrefs-hover: false - fig-responsive: true - footnotes-hover: true - lightbox: true - link-external-icon: true - link-external-newwindow: true - page-layout: article - page-navigation: true - reference-section-title: ' ' - page-footer: - left: 'Stephen J. Mildenhall. License: [CC BY-SA 2.0](https://creativecommons.org/licenses/by-sa/2.0/).' - twitter-card: true - open-graph: true - toc: true - toc-depth: 3 - math: mathjax - pdf: - include-in-header: prefobnicate.tex - documentclass: scrartcl - papersize: a4 - fontsize: 11pt - keep-tex: true - geometry: margin=0.8in - pdf-engine: lualatex - pdf-engine-opts: - - '-interaction=nonstopmode' - toc: false -execute: - eval: true - echo: true - cache: true - cache-type: jupyter - freeze: false - kernel: python3 - engine: jupyter - daemon: 1200 -jupyter: - jupytext: - formats: ipynb,qmd:quarto - text_representation: - extension: .qmd - format_name: quarto - format_version: '1.0' - jupytext_version: 1.16.4 - kernelspec: - display_name: Python 3 (ipykernel) - language: python - name: python3 ---- - -```{python} -#| echo: true -#| label: setup -from IPython.display import HTML, display -import matplotlib as mpl -import matplotlib.dates as mdates -import matplotlib.pyplot as plt -import numpy as np -import pandas as pd - -import greater_tables as gter -import greater_tables.utilities as gtu -from greater_tables import GT, sGT -gter.logger.setLevel(gter.logging.WARNING) -``` - -...code build completed. - -# A Hard-Rules table - -Second level index has mixed types. Range of magnitudes. Picking out years. - -\footnotesize - - -```{python} -#| label: tbl-hard-rules -#| tbl-cap: Default display output (Quarto generated caption) -level_1 = ["A", "A", "B", "B", 'C'] -level_2 = ['Int', 'Float', 'Float', 3, 'Longer Text'] - -multi_index = pd.MultiIndex.from_arrays([level_1, level_2], - names=["Level 1", "Level 2"]) -start = pd.Timestamp.today().normalize() # Today's date, normalized to midnight -end = pd.Timestamp(f"{start.year}-12-31") # End of the year - -hard = pd.DataFrame( -{'years!': np.arange(2000, 2025, dtype=int), -'a': np.array(np.round(np.linspace(-100000, 100000, 25), 0), dtype=int), -'b': 9.3 ** np.linspace(-12, 12, 25), -'c': np.linspace(-1601, 4000, 25), -'d': pd.date_range(start=start, end=end, periods=25), -'e': ('once upon a time, risk is hard to define, not in Kansas anymore, ' - 'neutrinos are hard to detect, ' - 'Adam Smith is the father of economics'.split(',') * 5) -}).set_index('years!') -# hard = hard.head() -hard.columns = multi_index -hard -``` - -\normalsize - -@tbl-hard-rules shows the default output and @tbl-hard-rules-2 the `sGT` format output. - -```{python} -#| label: tbl-hard-rules-2 -#| tbl-cap: Greater Tables output (Quarto generated caption) -sGT(hard, 'A table with varied columns.') -``` - -Here are some alternatives: - -* @tbl-hard-rules-3a hrules no vrules -* @tbl-hard-rules-3b change date and integer formats and -* @tbl-hard-rules-3c change padding and debug mode. - -```{python} -#| echo: fenced -#| label: tbl-hard-rules-3a -#| tbl-cap: No V rules but hrules (Quarto generated caption) -display(sGT(hard.sample(5).sort_index(), - caption='GT caption No v rules, but h rules', - vrule_widths=(0,0,0), - hrule_widths=(1,0,0))) -``` - -```{python} -#| echo: fenced -#| label: tbl-hard-rules-3b -#| tbl-cap: Change date and integer formats (Quarto generated caption) -display(sGT(hard.sample(5).sort_index(), - caption='Change default date and integer formats', - default_date_str='%m-%d', default_integer_str='[{x:d}]')) -``` - -```{python} -#| echo: fenced -#| label: tbl-hard-rules-3c -#| tbl-cap: Change padding and debug mode, boxes (Quarto generated caption) -display(sGT(hard.sample(5).sort_index(), - caption='Change padding, debug mode lines', - padding_trbl=(10, 10, 20, 20), debug=True)) -``` - -Here is the raw HTML and LaTeX output. - -\footnotesize - -```{python} -#| label: raw-output -f = sGT(hard.head(4), debug=True) -print('HTML output\n') -print(f._repr_html_()) - -print('\n\n\nTeX output\n') -print(f._repr_latex_()) -``` - -\normalsize - - -# A Table with TeX Content - -```{python} -#| label: tbl-tex -#| tbl-cap: '(Quarto generated caption): table displayed by default routine.' -index = pd.Index(["A", "B", "$C_1$", "C_2 not tex", '$\\cos(A)$']) -tex = pd.DataFrame( -{'x': np.arange(2020, 2025, dtype=int), -'b': np.random.random(5), -'a1': [f'$x^{i}$' for i in range(5,10)], -'a2': [f'$\\sin({i}x\\pi/n)$' for i in range(5,10)], -'a3': [f'$x^{i}$' for i in range(5,10)], -'a4': [f'\\(x^{i}\\)' for i in range(5,10)], -}).set_index('x') -tex = tex.head() -tex.columns = index -tex -``` - -```{python} -#| label: tbl-tex-2 -#| tbl-cap: GT output (Quarto generated caption) -sGT(tex, 'GT Caption') -``` - -Ratio columns. - -```{python} -#| label: tbl-tex-3 -#| tbl-cap: greater table output -tex.columns = ["A (%)", "B", "$C_1$", "C_2 not tex", '$\\cos(A)$'] -sGT(tex, 'Ratio columns in A', ratio_cols='A (%)') -``` - -# Greater_tables Test Suite - -```{python} -#| echo: true -#| label: greater-tables-test -test_gen = gtu.TestDFGenerator(0, 0) -ans = test_gen.test_suite() -``` - -## Test Table: basic - -```{python} -#| echo: true -#| label: tbl-greater-tables-test-0 -#| tbl-cap: GT output for test table basic -hrw = (0, 0, 0) -sGT(ans['basic'], "Basic", ratio_cols='z', aligners={'w': 'l'}, - hrule_widths=hrw) -``` - -Comments go here. - - - -## Test Table: timeseries - -```{python} -#| echo: true -#| label: tbl-greater-tables-test-1 -#| tbl-cap: GT output for test table timeseries -hrw = (0, 0, 0) -sGT(ans['timeseries'], "Timeseries", ratio_cols='z', aligners={'w': 'l'}, - hrule_widths=hrw) -``` - -Comments go here. - - - - -## Test Table: multiindex - -```{python} -#| echo: true -#| label: tbl-greater-tables-test-2 -#| tbl-cap: GT output for test table multiindex -hrw = (1.5, 1.0, 0.5) -sGT(ans['multiindex'], "Multiindex", ratio_cols='z', aligners={'w': 'l'}, - hrule_widths=hrw) -``` - -Comments go here. - - - - -## Test Table: multicolumns - -```{python} -#| echo: true -#| label: tbl-greater-tables-test-3 -#| tbl-cap: GT output for test table multicolumns -hrw = (0, 0, 0) -sGT(ans['multicolumns'], "Multicolumns", ratio_cols='z', aligners={'w': 'l'}, - hrule_widths=hrw) -``` - -Comments go here. - - - - -## Test Table: complex - -```{python} -#| echo: true -#| label: tbl-greater-tables-test-4 -#| tbl-cap: GT output for test table complex -hrw = (1.5, 1.0, 0.5) -sGT(ans['complex'], "Complex", ratio_cols='z', aligners={'w': 'l'}, - hrule_widths=hrw) -``` - -Comments go here. - -# Other input formats - -## Markown - -| **Insured group or insurance product** | **Sat** | **RP** | **RF** | -|:------------------------------------------------------------|:-------:|:------:|:------:| -| Non-standard auto | x | | | -| General liability for judgment proof corporation | x | | | -| Term life insurance | | x | | -| Catastrophe Reinsurance, outside rating agency bounds | | x | | -| High limit property per risk reinsurance | | x | | -| Personal lines for affluent individuals | x | x | | -| Small commercial lines | x | x | | -| Catastrophe reinsurance, within rating agency bounds | x | x | | -| Large account captive reinsurance | | | x | -| Structured quota share, requiring a risk transfer test | x | | x | -| Working layer casualty excess of loss | | x | x | -| Surplus relief quota share on cat exposed line | x | x | x | -| Middle market commercial lines work comp or commercial auto | x | x | x | - -```{python} -#| echo: true -#| label: tbl-greater-tables-test-5 -#| tbl-cap: GT from markdown table input -txt = ''' - -| **Insured group or insurance product** | **Sat** | **RP** | **RF** | -|:------------------------------------------------------------|:-------:|:------:|:------:| -| Non-standard auto | x | | | -| General liability for judgment proof corporation | x | | | -| Term life insurance | | x | | -| Catastrophe Reinsurance, outside rating agency bounds | | x | | -| High limit property per risk reinsurance | | x | | -| Personal lines for affluent individuals | x | x | | -| Small commercial lines | x | x | | -| Catastrophe reinsurance, within rating agency bounds | x | x | | -| Large account captive reinsurance | | | x | -| Structured quota share, requiring a risk transfer test | x | | x | -| Working layer casualty excess of loss | | x | x | -| Surplus relief quota share on cat exposed line | x | x | x | -| Middle market commercial lines work comp or commercial auto | x | x | x | - - -''' - -GT(txt) -``` - -## List of lists - -```{python} -x = None -if x: - print(123) -``` - -```{python} -#| echo: true -#| label: tbl-greater-tables-test-6 -#| tbl-cap: GT output for list of lists input -lol = [['a', 'b', 'c', 'd'], ['west', 10, 20, 30], ['east', 10, 200, 30], ['north', 10, 20, 300], ['south', 100, 20, 30]] -GT(lol) -``` - -```{python} -f = GT(lol) -f -``` - -```{python} -tbl = ''' - -Var | Amount -:---|------: -A | 100.0 -B | 0.123 -C | A string - -''' - -def ff(x): - if abs(x) < 1: - return f'{x:.1%}' - else: - return f'{x:,.2f}' - -sGT(tbl, table_float_format=ff) -``` - -```{python} -P = 1000 * 1.075**-10 + 120 -L = 1000 -ry = .1 -v = 1/(1+ry) -T = 10 -pv = P - v**T * L -fv = pv / v**T -pv, fv -``` - diff --git a/tests/tables.tex b/tests/tables.tex deleted file mode 100644 index 9845f60..0000000 --- a/tests/tables.tex +++ /dev/null @@ -1,1537 +0,0 @@ -% Options for packages loaded elsewhere -\PassOptionsToPackage{unicode}{hyperref} -\PassOptionsToPackage{hyphens}{url} -\PassOptionsToPackage{dvipsnames,svgnames,x11names}{xcolor} -% -\documentclass[ - 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Mildenhall}, - colorlinks=true, - linkcolor={blue}, - filecolor={Maroon}, - citecolor={Blue}, - urlcolor={Blue}, - pdfcreator={LaTeX via pandoc}} - - -\title{All Tables Test - New TestDFGenerator test\_suite} -\author{Stephen J. Mildenhall} -\date{2025-03-14} - -\begin{document} -\maketitle - - -\phantomsection\label{setup} -\begin{Shaded} -\begin{Highlighting}[] -\ImportTok{from}\NormalTok{ IPython.display }\ImportTok{import}\NormalTok{ HTML, display} -\ImportTok{import}\NormalTok{ matplotlib }\ImportTok{as}\NormalTok{ mpl} -\ImportTok{import}\NormalTok{ matplotlib.dates }\ImportTok{as}\NormalTok{ mdates} -\ImportTok{import}\NormalTok{ matplotlib.pyplot }\ImportTok{as}\NormalTok{ plt} -\ImportTok{import}\NormalTok{ numpy }\ImportTok{as}\NormalTok{ np} -\ImportTok{import}\NormalTok{ pandas }\ImportTok{as}\NormalTok{ pd} - -\ImportTok{import}\NormalTok{ greater\_tables }\ImportTok{as}\NormalTok{ gter} -\ImportTok{import}\NormalTok{ greater\_tables.utilities }\ImportTok{as}\NormalTok{ gtu} -\ImportTok{from}\NormalTok{ greater\_tables }\ImportTok{import}\NormalTok{ GT, sGT} -\NormalTok{gter.logger.setLevel(gter.logging.WARNING)} -\end{Highlighting} -\end{Shaded} - -\ldots code build completed. - -\section{A Hard-Rules table}\label{a-hard-rules-table} - -Second level index has mixed types. Range of magnitudes. Picking out -years. - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{level\_1 }\OperatorTok{=}\NormalTok{ [}\StringTok{"A"}\NormalTok{, }\StringTok{"A"}\NormalTok{, }\StringTok{"B"}\NormalTok{, }\StringTok{"B"}\NormalTok{, }\StringTok{\textquotesingle{}C\textquotesingle{}}\NormalTok{]} -\NormalTok{level\_2 }\OperatorTok{=}\NormalTok{ [}\StringTok{\textquotesingle{}Int\textquotesingle{}}\NormalTok{, }\StringTok{\textquotesingle{}Float\textquotesingle{}}\NormalTok{, }\StringTok{\textquotesingle{}Float\textquotesingle{}}\NormalTok{, }\DecValTok{3}\NormalTok{, }\StringTok{\textquotesingle{}Longer Text\textquotesingle{}}\NormalTok{]} - -\NormalTok{multi\_index }\OperatorTok{=}\NormalTok{ pd.MultiIndex.from\_arrays([level\_1, level\_2],} -\NormalTok{ names}\OperatorTok{=}\NormalTok{[}\StringTok{"Level 1"}\NormalTok{, }\StringTok{"Level 2"}\NormalTok{])} -\NormalTok{start }\OperatorTok{=}\NormalTok{ pd.Timestamp.today().normalize() }\CommentTok{\# Today\textquotesingle{}s date, normalized to midnight} -\NormalTok{end }\OperatorTok{=}\NormalTok{ pd.Timestamp(}\SpecialStringTok{f"}\SpecialCharTok{\{}\NormalTok{start}\SpecialCharTok{.}\NormalTok{year}\SpecialCharTok{\}}\SpecialStringTok{{-}12{-}31"}\NormalTok{) }\CommentTok{\# End of the year} - -\NormalTok{hard }\OperatorTok{=}\NormalTok{ pd.DataFrame(} -\NormalTok{\{}\StringTok{\textquotesingle{}years!\textquotesingle{}}\NormalTok{: np.arange(}\DecValTok{2000}\NormalTok{, }\DecValTok{2025}\NormalTok{, dtype}\OperatorTok{=}\BuiltInTok{int}\NormalTok{),} -\StringTok{\textquotesingle{}a\textquotesingle{}}\NormalTok{: np.array(np.}\BuiltInTok{round}\NormalTok{(np.linspace(}\OperatorTok{{-}}\DecValTok{100000}\NormalTok{, }\DecValTok{100000}\NormalTok{, }\DecValTok{25}\NormalTok{), }\DecValTok{0}\NormalTok{), dtype}\OperatorTok{=}\BuiltInTok{int}\NormalTok{),} -\StringTok{\textquotesingle{}b\textquotesingle{}}\NormalTok{: }\FloatTok{9.3} \OperatorTok{**}\NormalTok{ np.linspace(}\OperatorTok{{-}}\DecValTok{12}\NormalTok{, }\DecValTok{12}\NormalTok{, }\DecValTok{25}\NormalTok{),} -\StringTok{\textquotesingle{}c\textquotesingle{}}\NormalTok{: np.linspace(}\OperatorTok{{-}}\DecValTok{1601}\NormalTok{, }\DecValTok{4000}\NormalTok{, }\DecValTok{25}\NormalTok{),} -\StringTok{\textquotesingle{}d\textquotesingle{}}\NormalTok{: pd.date\_range(start}\OperatorTok{=}\NormalTok{start, end}\OperatorTok{=}\NormalTok{end, periods}\OperatorTok{=}\DecValTok{25}\NormalTok{),} -\StringTok{\textquotesingle{}e\textquotesingle{}}\NormalTok{: (}\StringTok{\textquotesingle{}once upon a time, risk is hard to define, not in Kansas anymore, \textquotesingle{}} - \StringTok{\textquotesingle{}neutrinos are hard to detect, \textquotesingle{}} - \StringTok{\textquotesingle{}Adam Smith is the father of economics\textquotesingle{}}\NormalTok{.split(}\StringTok{\textquotesingle{},\textquotesingle{}}\NormalTok{) }\OperatorTok{*} \DecValTok{5}\NormalTok{)} -\NormalTok{\}).set\_index(}\StringTok{\textquotesingle{}years!\textquotesingle{}}\NormalTok{)} -\CommentTok{\# hard = hard.head()} -\NormalTok{hard.columns }\OperatorTok{=}\NormalTok{ multi\_index} -\NormalTok{hard} -\end{Highlighting} -\end{Shaded} - -\begin{longtable}[]{@{}llllll@{}} - -\caption{\label{tbl-hard-rules}Default display output (Quarto generated -caption)} - -\tabularnewline - -\toprule\noalign{} -Level 1 & \multicolumn{2}{l}{% -A} & \multicolumn{2}{l}{% -B} & C \\ -Level 2 & Int & Float & Float & 3 & Longer Text \\ -years! & & & & & \\ -\midrule\noalign{} -\endhead -\bottomrule\noalign{} -\endlastfoot -2000 & -100000 & 2.388937e-12 & -1601.000 & 2025-03-14 00:00:00 & once -upon a time \\ -2001 & -91667 & 2.221711e-11 & -1367.625 & 2025-03-26 04:00:00 & risk is -hard to define \\ -2002 & -83333 & 2.066191e-10 & -1134.250 & 2025-04-07 08:00:00 & not in -Kansas anymore \\ -2003 & -75000 & 1.921558e-09 & -900.875 & 2025-04-19 12:00:00 & -neutrinos are hard to detect \\ -2004 & -66667 & 1.787049e-08 & -667.500 & 2025-05-01 16:00:00 & Adam -Smith is the father of economics \\ -2005 & -58333 & 1.661955e-07 & -434.125 & 2025-05-13 20:00:00 & once -upon a time \\ -2006 & -50000 & 1.545619e-06 & -200.750 & 2025-05-26 00:00:00 & risk is -hard to define \\ -2007 & -41667 & 1.437425e-05 & 32.625 & 2025-06-07 04:00:00 & not in -Kansas anymore \\ -2008 & -33333 & 1.336805e-04 & 266.000 & 2025-06-19 08:00:00 & neutrinos -are hard to detect \\ -2009 & -25000 & 1.243229e-03 & 499.375 & 2025-07-01 12:00:00 & Adam -Smith is the father of economics \\ -2010 & -16667 & 1.156203e-02 & 732.750 & 2025-07-13 16:00:00 & once upon -a time \\ -2011 & -8333 & 1.075269e-01 & 966.125 & 2025-07-25 20:00:00 & risk is -hard to define \\ -2012 & 0 & 1.000000e+00 & 1199.500 & 2025-08-07 00:00:00 & not in Kansas -anymore \\ -2013 & 8333 & 9.300000e+00 & 1432.875 & 2025-08-19 04:00:00 & neutrinos -are hard to detect \\ -2014 & 16667 & 8.649000e+01 & 1666.250 & 2025-08-31 08:00:00 & Adam -Smith is the father of economics \\ -2015 & 25000 & 8.043570e+02 & 1899.625 & 2025-09-12 12:00:00 & once upon -a time \\ -2016 & 33333 & 7.480520e+03 & 2133.000 & 2025-09-24 16:00:00 & risk is -hard to define \\ -2017 & 41667 & 6.956884e+04 & 2366.375 & 2025-10-06 20:00:00 & not in -Kansas anymore \\ -2018 & 50000 & 6.469902e+05 & 2599.750 & 2025-10-19 00:00:00 & neutrinos -are hard to detect \\ -2019 & 58333 & 6.017009e+06 & 2833.125 & 2025-10-31 04:00:00 & Adam -Smith is the father of economics \\ -2020 & 66667 & 5.595818e+07 & 3066.500 & 2025-11-12 08:00:00 & once upon -a time \\ -2021 & 75000 & 5.204111e+08 & 3299.875 & 2025-11-24 12:00:00 & risk is -hard to define \\ -2022 & 83333 & 4.839823e+09 & 3533.250 & 2025-12-06 16:00:00 & not in -Kansas anymore \\ -2023 & 91667 & 4.501035e+10 & 3766.625 & 2025-12-18 20:00:00 & neutrinos -are hard to detect \\ -2024 & 100000 & 4.185963e+11 & 4000.000 & 2025-12-31 00:00:00 & Adam -Smith is the father of economics \\ - -\end{longtable} - -Table~\ref{tbl-hard-rules} shows the default output and -Table~\ref{tbl-hard-rules-2} the \texttt{sGT} format output. - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{sGT(hard, }\StringTok{\textquotesingle{}A table with varied columns.\textquotesingle{}}\NormalTok{)} -\end{Highlighting} -\end{Shaded} - -\begin{table} - -\caption{\label{tbl-hard-rules-2}Greater Tables output (Quarto generated -caption)} - -\begin{tikzpicture}[ - auto, - transform shape, - nosep/.style={inner sep=0}, - table/.style={ - matrix of nodes, - row sep=0.125em, - column sep=0.375em, - nodes in empty cells, - nodes={rectangle, scale=0.635, text badly ragged }, - row 1/.style={nodes={text=black, anchor=north, inner ysep=0, text height=0, text depth=0}}, - row 2/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}}, - row 3/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}}, - column 1/.style={nodes={align=left }, text height=0.9em, text depth=0.2em, inner xsep=0.375em, inner ysep=0, text width=3.60em}, - column 2/.style={nodes={align=right }, nosep, text width=5.71em}, - column 3/.style={nodes={align=right }, nosep, text width=6.43em}, - column 4/.style={nodes={align=right }, nosep, text width=6.43em}, - column 5/.style={nodes={align=center}, nosep, text width=7.14em}, - column 6/.style={nodes={align=left }, nosep, text width=27.85em}, - column 7/.style={text height=0.9em, text depth=0.2em, nosep, text width=0em} }] -\matrix (T4JQAJ5YI3QMU) [table, ampersand replacement=\&]{ - \& \& \& \& \& \& \\ - \grtspacer \& A\grtspacer \& \grtspacer \& B\grtspacer \& \grtspacer \& C\grtspacer \& \\ - years!\grtspacer \& Int\grtspacer \& Float\grtspacer \& Float\grtspacer \& 3\grtspacer \& Longer Text\grtspacer \& \\ - 2000 \& -100,000 \& 2.389p \& -1,601.00 \& 2025-03-14 \& once upon a time \& \\ - 2001 \& -91,667 \& 22.217p \& -1,367.62 \& 2025-03-26 \& risk is hard to define \& \\ - 2002 \& -83,333 \& 206.619p \& -1,134.25 \& 2025-04-07 \& not in Kansas anymore \& \\ - 2003 \& -75,000 \& 1.922n \& -900.88 \& 2025-04-19 \& neutrinos are hard to detect \& \\ - 2004 \& -66,667 \& 17.870n \& -667.50 \& 2025-05-01 \& Adam Smith is the father of economics \& \\ - 2005 \& -58,333 \& 166.196n \& -434.12 \& 2025-05-13 \& once upon a time \& \\ - 2006 \& -50,000 \& 1.546u \& -200.75 \& 2025-05-26 \& risk is hard to define \& \\ - 2007 \& -41,667 \& 14.374u \& 32.62 \& 2025-06-07 \& not in Kansas anymore \& \\ - 2008 \& -33,333 \& 133.681u \& 266.00 \& 2025-06-19 \& neutrinos are hard to detect \& \\ - 2009 \& -25,000 \& 1.243m \& 499.38 \& 2025-07-01 \& Adam Smith is the father of economics \& \\ - 2010 \& -16,667 \& 11.562m \& 732.75 \& 2025-07-13 \& once upon a time \& \\ - 2011 \& -8,333 \& 107.527m \& 966.12 \& 2025-07-25 \& risk is hard to define \& \\ - 2012 \& 0 \& 1.000 \& 1,199.50 \& 2025-08-07 \& not in Kansas anymore \& \\ - 2013 \& 8,333 \& 9.300 \& 1,432.88 \& 2025-08-19 \& neutrinos are hard to detect \& \\ - 2014 \& 16,667 \& 86.490 \& 1,666.25 \& 2025-08-31 \& Adam Smith is the father of economics \& \\ - 2015 \& 25,000 \& 804.357 \& 1,899.62 \& 2025-09-12 \& once upon a time \& \\ - 2016 \& 33,333 \& 7.481k \& 2,133.00 \& 2025-09-24 \& risk is hard to define \& \\ - 2017 \& 41,667 \& 69.569k \& 2,366.38 \& 2025-10-06 \& not in Kansas anymore \& \\ - 2018 \& 50,000 \& 646.990k \& 2,599.75 \& 2025-10-19 \& neutrinos are hard to detect \& \\ - 2019 \& 58,333 \& 6.017M \& 2,833.12 \& 2025-10-31 \& Adam Smith is the father of economics \& \\ - 2020 \& 66,667 \& 55.958M \& 3,066.50 \& 2025-11-12 \& once upon a time \& \\ - 2021 \& 75,000 \& 520.411M \& 3,299.88 \& 2025-11-24 \& risk is hard to define \& \\ - 2022 \& 83,333 \& 4.840G \& 3,533.25 \& 2025-12-06 \& not in Kansas anymore \& \\ - 2023 \& 91,667 \& 45.010G \& 3,766.62 \& 2025-12-18 \& neutrinos are hard to detect \& \\ - 2024 \& 100,000 \& 418.596G \& 4,000.00 \& 2025-12-31 \& Adam Smith is the father of economics \& \\ -}; - -\path[draw, thick] (T4JQAJ5YI3QMU-1-1.south west) -- (T4JQAJ5YI3QMU-1-7.south east); -\path[draw, semithick] ([yshift=-0.0625em]T4JQAJ5YI3QMU-3-1.south west) -- ([yshift=-0.0625em]T4JQAJ5YI3QMU-3-7.south east); -\path[draw, thick] ([yshift=-0.3125em]T4JQAJ5YI3QMU-28-1.base west) -- ([yshift=-0.3125em]T4JQAJ5YI3QMU-28-7.base east); -\path[draw, very thin] ([xshift=-0.1875em, yshift=-0.0625em]T4JQAJ5YI3QMU-2-2.south west) -- ([yshift=-0.0625em]T4JQAJ5YI3QMU-2-7.south east); -\path[draw, very thin] ([xshift=-0.1875em]T4JQAJ5YI3QMU-1-2.south west) -- ([yshift=-0.3125em, xshift=-0.1875em]T4JQAJ5YI3QMU-28-2.base west); -\path[draw, ultra thin] ([xshift=0.1875em, yshift=-0.0625em]T4JQAJ5YI3QMU-1-3.south east) -- ([yshift=-0.3125em, xshift=0.1875em]T4JQAJ5YI3QMU-28-3.base east); -\path[draw, ultra thin] ([xshift=0.1875em, yshift=-0.0625em]T4JQAJ5YI3QMU-1-5.south east) -- ([yshift=-0.3125em, xshift=0.1875em]T4JQAJ5YI3QMU-28-5.base east); - - - -\end{tikzpicture} - -\end{table}% - -Here are some alternatives: - -\begin{itemize} -\tightlist -\item - Table~\ref{tbl-hard-rules-3a} hrules no vrules -\item - Table~\ref{tbl-hard-rules-3b} change date and integer formats and -\item - Table~\ref{tbl-hard-rules-3c} change padding and debug mode. -\end{itemize} - -\begin{Shaded} -\begin{Highlighting}[] -\InformationTok{\textasciigrave{}\textasciigrave{}\textasciigrave{}\{python\}} -\InformationTok{\#| label: tbl{-}hard{-}rules{-}3a} -\InformationTok{\#| tbl{-}cap: No V rules but hrules (Quarto generated caption)} -\InformationTok{display(sGT(hard.sample(5).sort\_index(),} -\InformationTok{ caption=\textquotesingle{}GT caption No v rules, but h rules\textquotesingle{},} -\InformationTok{ vrule\_widths=(0,0,0),} -\InformationTok{ hrule\_widths=(1,0,0)))} -\InformationTok{\textasciigrave{}\textasciigrave{}\textasciigrave{}} -\end{Highlighting} -\end{Shaded} - -\begin{table} - -\caption{\label{tbl-hard-rules-3a}No V rules but hrules (Quarto -generated caption)} - -\begin{tikzpicture}[ - auto, - transform shape, - nosep/.style={inner sep=0}, - table/.style={ - matrix of nodes, - row sep=0.125em, - column sep=0.375em, - nodes in empty cells, - nodes={rectangle, scale=0.635, text badly ragged }, - row 1/.style={nodes={text=black, anchor=north, inner ysep=0, text height=0, text depth=0}}, - row 2/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}}, - row 3/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}}, - column 1/.style={nodes={align=left }, text height=0.9em, text depth=0.2em, inner xsep=0.375em, inner ysep=0, text width=3.60em}, - column 2/.style={nodes={align=right }, nosep, text width=5.13em}, - column 3/.style={nodes={align=right }, nosep, text width=6.60em}, - column 4/.style={nodes={align=right }, nosep, text width=5.87em}, - column 5/.style={nodes={align=center}, nosep, text width=7.34em}, - column 6/.style={nodes={align=left }, nosep, text width=28.61em}, - column 7/.style={text height=0.9em, text depth=0.2em, nosep, text width=0em} }] -\matrix (TDYK7WPLIAE7W) [table, ampersand replacement=\&]{ - \& \& \& \& \& \& \\ - \grtspacer \& A\grtspacer \& \grtspacer \& B\grtspacer \& \grtspacer \& C\grtspacer \& \\ - years!\grtspacer \& Int\grtspacer \& Float\grtspacer \& Float\grtspacer \& 3\grtspacer \& Longer Text\grtspacer \& \\ - 2008 \& -33,333 \& 133.681u \& 266.00 \& 2025-06-19 \& neutrinos are hard to detect \& \\ - 2010 \& -16,667 \& 11.562m \& 732.75 \& 2025-07-13 \& once upon a time \& \\ - 2020 \& 66,667 \& 55.958M \& 3,066.50 \& 2025-11-12 \& once upon a time \& \\ - 2021 \& 75,000 \& 520.411M \& 3,299.88 \& 2025-11-24 \& risk is hard to define \& \\ - 2024 \& 100,000 \& 418.596G \& 4,000.00 \& 2025-12-31 \& Adam Smith is the father of economics \& \\ -}; - -\path[draw, thick] (TDYK7WPLIAE7W-1-1.south west) -- (TDYK7WPLIAE7W-1-7.south east); -\path[draw, semithick] ([yshift=-0.0625em]TDYK7WPLIAE7W-3-1.south west) -- ([yshift=-0.0625em]TDYK7WPLIAE7W-3-7.south east); -\path[draw, thick] ([yshift=-0.3125em]TDYK7WPLIAE7W-8-1.base west) -- ([yshift=-0.3125em]TDYK7WPLIAE7W-8-7.base east); -\path[draw, very thin] ([xshift=-0.1875em, yshift=-0.0625em]TDYK7WPLIAE7W-2-2.south west) -- ([yshift=-0.0625em]TDYK7WPLIAE7W-2-7.south east); -\path[draw, very thin] ([xshift=-0.1875em]TDYK7WPLIAE7W-1-2.south west) -- ([yshift=-0.3125em, xshift=-0.1875em]TDYK7WPLIAE7W-8-2.base west); -\path[draw, ultra thin] ([xshift=0.1875em, yshift=-0.0625em]TDYK7WPLIAE7W-1-3.south east) -- ([yshift=-0.3125em, xshift=0.1875em]TDYK7WPLIAE7W-8-3.base east); -\path[draw, ultra thin] ([xshift=0.1875em, yshift=-0.0625em]TDYK7WPLIAE7W-1-5.south east) -- ([yshift=-0.3125em, xshift=0.1875em]TDYK7WPLIAE7W-8-5.base east); - - - -\end{tikzpicture} - -\end{table}% - -\begin{Shaded} -\begin{Highlighting}[] -\InformationTok{\textasciigrave{}\textasciigrave{}\textasciigrave{}\{python\}} -\InformationTok{\#| label: tbl{-}hard{-}rules{-}3b} -\InformationTok{\#| tbl{-}cap: Change date and integer formats (Quarto generated caption)} -\InformationTok{display(sGT(hard.sample(5).sort\_index(),} -\InformationTok{ caption=\textquotesingle{}Change default date and integer formats\textquotesingle{},} -\InformationTok{ default\_date\_str=\textquotesingle{}\%m{-}\%d\textquotesingle{}, default\_integer\_str=\textquotesingle{}[\{x:d\}]\textquotesingle{}))} -\InformationTok{\textasciigrave{}\textasciigrave{}\textasciigrave{}} -\end{Highlighting} -\end{Shaded} - -\begin{table} - -\caption{\label{tbl-hard-rules-3b}Change date and integer formats -(Quarto generated caption)} - -\begin{tikzpicture}[ - auto, - transform shape, - nosep/.style={inner sep=0}, - table/.style={ - matrix of nodes, - row sep=0.125em, - column sep=0.375em, - nodes in empty cells, - nodes={rectangle, scale=0.635, text badly ragged }, - row 1/.style={nodes={text=black, anchor=north, inner ysep=0, text height=0, text depth=0}}, - row 2/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}}, - row 3/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}}, - column 1/.style={nodes={align=left }, text height=0.9em, text depth=0.2em, inner xsep=0.375em, inner ysep=0, text width=3.60em}, - column 2/.style={nodes={align=right }, nosep, text width=6.21em}, - column 3/.style={nodes={align=right }, nosep, text width=6.21em}, - column 4/.style={nodes={align=right }, nosep, text width=6.98em}, - column 5/.style={nodes={align=center}, nosep, text width=3.88em}, - column 6/.style={nodes={align=left }, nosep, text width=30.27em}, - column 7/.style={text height=0.9em, text depth=0.2em, nosep, text width=0em} }] -\matrix (TVL35CCVTDDBB) [table, ampersand replacement=\&]{ - \& \& \& \& \& \& \\ - \grtspacer \& A\grtspacer \& \grtspacer \& B\grtspacer \& \grtspacer \& C\grtspacer \& \\ - years!\grtspacer \& Int\grtspacer \& Float\grtspacer \& Float\grtspacer \& 3\grtspacer \& Longer Text\grtspacer \& \\ - 2001 \& [-91667] \& 22.217p \& -1,367.62 \& 03-26 \& risk is hard to define \& \\ - 2009 \& [-25000] \& 1.243m \& 499.38 \& 07-01 \& Adam Smith is the father of economics \& \\ - 2017 \& [41667] \& 69.569k \& 2,366.38 \& 10-06 \& not in Kansas anymore \& \\ - 2019 \& [58333] \& 6.017M \& 2,833.12 \& 10-31 \& Adam Smith is the father of economics \& \\ - 2023 \& [91667] \& 45.010G \& 3,766.62 \& 12-18 \& neutrinos are hard to detect \& \\ -}; - -\path[draw, thick] (TVL35CCVTDDBB-1-1.south west) -- (TVL35CCVTDDBB-1-7.south east); -\path[draw, semithick] ([yshift=-0.0625em]TVL35CCVTDDBB-3-1.south west) -- ([yshift=-0.0625em]TVL35CCVTDDBB-3-7.south east); -\path[draw, thick] ([yshift=-0.3125em]TVL35CCVTDDBB-8-1.base west) -- ([yshift=-0.3125em]TVL35CCVTDDBB-8-7.base east); -\path[draw, very thin] ([xshift=-0.1875em, yshift=-0.0625em]TVL35CCVTDDBB-2-2.south west) -- ([yshift=-0.0625em]TVL35CCVTDDBB-2-7.south east); -\path[draw, very thin] ([xshift=-0.1875em]TVL35CCVTDDBB-1-2.south west) -- ([yshift=-0.3125em, xshift=-0.1875em]TVL35CCVTDDBB-8-2.base west); -\path[draw, ultra thin] ([xshift=0.1875em, yshift=-0.0625em]TVL35CCVTDDBB-1-3.south east) -- ([yshift=-0.3125em, xshift=0.1875em]TVL35CCVTDDBB-8-3.base east); -\path[draw, ultra thin] ([xshift=0.1875em, yshift=-0.0625em]TVL35CCVTDDBB-1-5.south east) -- ([yshift=-0.3125em, xshift=0.1875em]TVL35CCVTDDBB-8-5.base east); - - - -\end{tikzpicture} - -\end{table}% - -\begin{Shaded} -\begin{Highlighting}[] -\InformationTok{\textasciigrave{}\textasciigrave{}\textasciigrave{}\{python\}} -\InformationTok{\#| label: tbl{-}hard{-}rules{-}3c} -\InformationTok{\#| tbl{-}cap: Change padding and debug mode, boxes (Quarto generated caption)} -\InformationTok{display(sGT(hard.sample(5).sort\_index(),} -\InformationTok{ caption=\textquotesingle{}Change padding, debug mode lines\textquotesingle{},} -\InformationTok{ padding\_trbl=(10, 10, 20, 20), debug=True))} -\InformationTok{\textasciigrave{}\textasciigrave{}\textasciigrave{}} -\end{Highlighting} -\end{Shaded} - -\begin{table} - -\caption{\label{tbl-hard-rules-3c}Change padding and debug mode, boxes -(Quarto generated caption)} - -\begin{tikzpicture}[ - auto, - transform shape, - nosep/.style={inner sep=0}, - table/.style={ - matrix of nodes, - row sep=0.125em, - column sep=0.375em, - nodes in empty cells, - nodes={rectangle, scale=0.635, text badly ragged , draw=blue!10}, - row 1/.style={nodes={text=black, anchor=north, inner ysep=0, text height=0, text depth=0}}, - row 2/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}}, - row 3/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}}, - column 1/.style={nodes={align=left }, text height=0.9em, text depth=0.2em, inner xsep=0.375em, inner ysep=0, text width=3.60em}, - column 2/.style={nodes={align=right }, nosep, text width=5.71em}, - column 3/.style={nodes={align=right }, nosep, text width=6.43em}, - column 4/.style={nodes={align=right }, nosep, text width=6.43em}, - column 5/.style={nodes={align=center}, nosep, text width=7.14em}, - column 6/.style={nodes={align=left }, nosep, text width=27.85em}, - column 7/.style={text height=0.9em, text depth=0.2em, nosep, text width=0em} }] -\matrix (TGTVSPSJTJM2I) [table, ampersand replacement=\&]{ - \& \& \& \& \& \& \\ - \grtspacer \& A\grtspacer \& \grtspacer \& B\grtspacer \& \grtspacer \& C\grtspacer \& \\ - years!\grtspacer \& Int\grtspacer \& Float\grtspacer \& Float\grtspacer \& 3\grtspacer \& Longer Text\grtspacer \& \\ - 2000 \& -100,000 \& 2.389p \& -1,601.00 \& 2025-03-14 \& once upon a time \& \\ - 2003 \& -75,000 \& 1.922n \& -900.88 \& 2025-04-19 \& neutrinos are hard to detect \& \\ - 2004 \& -66,667 \& 17.870n \& -667.50 \& 2025-05-01 \& Adam Smith is the father of economics \& \\ - 2005 \& -58,333 \& 166.196n \& -434.12 \& 2025-05-13 \& once upon a time \& \\ - 2023 \& 91,667 \& 45.010G \& 3,766.62 \& 2025-12-18 \& neutrinos are hard to detect \& \\ -}; - -\path[draw, thick] (TGTVSPSJTJM2I-1-1.south west) -- (TGTVSPSJTJM2I-1-7.south east); -\path[draw, semithick] ([yshift=-0.0625em]TGTVSPSJTJM2I-3-1.south west) -- ([yshift=-0.0625em]TGTVSPSJTJM2I-3-7.south east); -\path[draw, thick] ([yshift=-0.3125em]TGTVSPSJTJM2I-8-1.base west) -- ([yshift=-0.3125em]TGTVSPSJTJM2I-8-7.base east); -\path[draw, very thin] ([xshift=-0.1875em, yshift=-0.0625em]TGTVSPSJTJM2I-2-2.south west) -- ([yshift=-0.0625em]TGTVSPSJTJM2I-2-7.south east); -\path[draw, very thin] ([xshift=-0.1875em]TGTVSPSJTJM2I-1-2.south west) -- ([yshift=-0.3125em, xshift=-0.1875em]TGTVSPSJTJM2I-8-2.base west); -\path[draw, ultra thin] ([xshift=0.1875em, yshift=-0.0625em]TGTVSPSJTJM2I-1-3.south east) -- ([yshift=-0.3125em, xshift=0.1875em]TGTVSPSJTJM2I-8-3.base east); -\path[draw, ultra thin] ([xshift=0.1875em, yshift=-0.0625em]TGTVSPSJTJM2I-1-5.south east) -- ([yshift=-0.3125em, xshift=0.1875em]TGTVSPSJTJM2I-8-5.base east); - - - -\end{tikzpicture} - -\end{table}% - -Here is the raw HTML and LaTeX output. - -\footnotesize - -\phantomsection\label{raw-output} -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{f }\OperatorTok{=}\NormalTok{ sGT(hard.head(}\DecValTok{4}\NormalTok{), debug}\OperatorTok{=}\VariableTok{True}\NormalTok{)} -\BuiltInTok{print}\NormalTok{(}\StringTok{\textquotesingle{}HTML output}\CharTok{\textbackslash{}n}\StringTok{\textquotesingle{}}\NormalTok{)} -\BuiltInTok{print}\NormalTok{(f.\_repr\_html\_())} - -\BuiltInTok{print}\NormalTok{(}\StringTok{\textquotesingle{}}\CharTok{\textbackslash{}n\textbackslash{}n\textbackslash{}n}\StringTok{TeX output}\CharTok{\textbackslash{}n}\StringTok{\textquotesingle{}}\NormalTok{)} -\BuiltInTok{print}\NormalTok{(f.\_repr\_latex\_())} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -HTML output - -
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
(id: T6JW65HYNG3A5)
ABC
years!IntFloatFloat3Longer Text
2000-100,000 2.389p-1,601.002025-03-14once upon a time
2001-91,667 22.217p-1,367.622025-03-26 risk is hard to define
2002-83,333 206.619p-1,134.252025-04-07 not in Kansas anymore
2003-75,000 1.922n-900.882025-04-19 neutrinos are hard to detect
- - - -TeX output - - -\begin{tikzpicture}[ - auto, - transform shape, - nosep/.style={inner sep=0}, - table/.style={ - matrix of nodes, - row sep=0.125em, - column sep=0.375em, - nodes in empty cells, - nodes={rectangle, scale=0.635, text badly ragged , draw=blue!10}, - row 1/.style={nodes={text=black, anchor=north, inner ysep=0, text height=0, text depth=0}}, - row 2/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}}, - row 3/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}}, - column 1/.style={nodes={align=left }, text height=0.9em, text depth=0.2em, inner xsep=0.375em, inner ysep=0, text width=3.60em}, - column 2/.style={nodes={align=right }, nosep, text width=6.59em}, - column 3/.style={nodes={align=right }, nosep, text width=7.41em}, - column 4/.style={nodes={align=right }, nosep, text width=7.41em}, - column 5/.style={nodes={align=center}, nosep, text width=8.24em}, - column 6/.style={nodes={align=left }, nosep, text width=23.89em}, - column 7/.style={text height=0.9em, text depth=0.2em, nosep, text width=0em} }] -\matrix (T6JW65HYNG3A5) [table, ampersand replacement=\&]{ - \& \& \& \& \& \& \\ - \grtspacer \& A\grtspacer \& \grtspacer \& B\grtspacer \& \grtspacer \& C\grtspacer \& \\ - years!\grtspacer \& Int\grtspacer \& Float\grtspacer \& Float\grtspacer \& 3\grtspacer \& Longer Text\grtspacer \& \\ - 2000 \& -100,000 \& 2.389p \& -1,601.00 \& 2025-03-14 \& once upon a time \& \\ - 2001 \& -91,667 \& 22.217p \& -1,367.62 \& 2025-03-26 \& risk is hard to define \& \\ - 2002 \& -83,333 \& 206.619p \& -1,134.25 \& 2025-04-07 \& not in Kansas anymore \& \\ - 2003 \& -75,000 \& 1.922n \& -900.88 \& 2025-04-19 \& neutrinos are hard to detect \& \\ -}; - -\path[draw, thick] (T6JW65HYNG3A5-1-1.south west) -- (T6JW65HYNG3A5-1-7.south east); -\path[draw, semithick] ([yshift=-0.0625em]T6JW65HYNG3A5-3-1.south west) -- ([yshift=-0.0625em]T6JW65HYNG3A5-3-7.south east); -\path[draw, thick] ([yshift=-0.3125em]T6JW65HYNG3A5-7-1.base west) -- ([yshift=-0.3125em]T6JW65HYNG3A5-7-7.base east); -\path[draw, very thin] ([xshift=-0.1875em, yshift=-0.0625em]T6JW65HYNG3A5-2-2.south west) -- ([yshift=-0.0625em]T6JW65HYNG3A5-2-7.south east); -\path[draw, very thin] ([xshift=-0.1875em]T6JW65HYNG3A5-1-2.south west) -- ([yshift=-0.3125em, xshift=-0.1875em]T6JW65HYNG3A5-7-2.base west); -\path[draw, ultra thin] ([xshift=0.1875em, yshift=-0.0625em]T6JW65HYNG3A5-1-3.south east) -- ([yshift=-0.3125em, xshift=0.1875em]T6JW65HYNG3A5-7-3.base east); -\path[draw, ultra thin] ([xshift=0.1875em, yshift=-0.0625em]T6JW65HYNG3A5-1-5.south east) -- ([yshift=-0.3125em, xshift=0.1875em]T6JW65HYNG3A5-7-5.base east); - - - -\end{tikzpicture} -\end{verbatim} - -\normalsize - -\section{A Table with TeX Content}\label{a-table-with-tex-content} - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{index }\OperatorTok{=}\NormalTok{ pd.Index([}\StringTok{"A"}\NormalTok{, }\StringTok{"B"}\NormalTok{, }\StringTok{"$C\_1$"}\NormalTok{, }\StringTok{"C\_2 not tex"}\NormalTok{, }\StringTok{\textquotesingle{}$}\CharTok{\textbackslash{}\textbackslash{}}\StringTok{cos(A)$\textquotesingle{}}\NormalTok{])} -\NormalTok{tex }\OperatorTok{=}\NormalTok{ pd.DataFrame(} -\NormalTok{\{}\StringTok{\textquotesingle{}x\textquotesingle{}}\NormalTok{: np.arange(}\DecValTok{2020}\NormalTok{, }\DecValTok{2025}\NormalTok{, dtype}\OperatorTok{=}\BuiltInTok{int}\NormalTok{),} -\StringTok{\textquotesingle{}b\textquotesingle{}}\NormalTok{: np.random.random(}\DecValTok{5}\NormalTok{),} -\StringTok{\textquotesingle{}a1\textquotesingle{}}\NormalTok{: [}\SpecialStringTok{f\textquotesingle{}$x\^{}}\SpecialCharTok{\{}\NormalTok{i}\SpecialCharTok{\}}\SpecialStringTok{$\textquotesingle{}} \ControlFlowTok{for}\NormalTok{ i }\KeywordTok{in} \BuiltInTok{range}\NormalTok{(}\DecValTok{5}\NormalTok{,}\DecValTok{10}\NormalTok{)],} -\StringTok{\textquotesingle{}a2\textquotesingle{}}\NormalTok{: [}\SpecialStringTok{f\textquotesingle{}$}\CharTok{\textbackslash{}\textbackslash{}}\SpecialStringTok{sin(}\SpecialCharTok{\{}\NormalTok{i}\SpecialCharTok{\}}\SpecialStringTok{x}\CharTok{\textbackslash{}\textbackslash{}}\SpecialStringTok{pi/n)$\textquotesingle{}} \ControlFlowTok{for}\NormalTok{ i }\KeywordTok{in} \BuiltInTok{range}\NormalTok{(}\DecValTok{5}\NormalTok{,}\DecValTok{10}\NormalTok{)],} -\StringTok{\textquotesingle{}a3\textquotesingle{}}\NormalTok{: [}\SpecialStringTok{f\textquotesingle{}$x\^{}}\SpecialCharTok{\{}\NormalTok{i}\SpecialCharTok{\}}\SpecialStringTok{$\textquotesingle{}} \ControlFlowTok{for}\NormalTok{ i }\KeywordTok{in} \BuiltInTok{range}\NormalTok{(}\DecValTok{5}\NormalTok{,}\DecValTok{10}\NormalTok{)],} -\StringTok{\textquotesingle{}a4\textquotesingle{}}\NormalTok{: [}\SpecialStringTok{f\textquotesingle{}}\CharTok{\textbackslash{}\textbackslash{}}\SpecialStringTok{(x\^{}}\SpecialCharTok{\{}\NormalTok{i}\SpecialCharTok{\}}\CharTok{\textbackslash{}\textbackslash{}}\SpecialStringTok{)\textquotesingle{}} \ControlFlowTok{for}\NormalTok{ i }\KeywordTok{in} \BuiltInTok{range}\NormalTok{(}\DecValTok{5}\NormalTok{,}\DecValTok{10}\NormalTok{)],} -\NormalTok{\}).set\_index(}\StringTok{\textquotesingle{}x\textquotesingle{}}\NormalTok{)} -\NormalTok{tex }\OperatorTok{=}\NormalTok{ tex.head()} -\NormalTok{tex.columns }\OperatorTok{=}\NormalTok{ index} -\NormalTok{tex} -\end{Highlighting} -\end{Shaded} - -\begin{longtable}[]{@{}llllll@{}} - -\caption{\label{tbl-tex}(Quarto generated caption): table displayed by -default routine.} - -\tabularnewline - -\toprule\noalign{} -& A & B & \$C\_1\$ & C\_2 not tex & \$\textbackslash cos(A)\$ \\ -x & & & & & \\ -\midrule\noalign{} -\endhead -\bottomrule\noalign{} -\endlastfoot -2020 & 0.501120 & \$x\^{}5\$ & -\$\textbackslash sin(5x\textbackslash pi/n)\$ & \$x\^{}5\$ & -\textbackslash(x\^{}5\textbackslash) \\ -2021 & 0.337571 & \$x\^{}6\$ & -\$\textbackslash sin(6x\textbackslash pi/n)\$ & \$x\^{}6\$ & -\textbackslash(x\^{}6\textbackslash) \\ -2022 & 0.869421 & \$x\^{}7\$ & -\$\textbackslash sin(7x\textbackslash pi/n)\$ & \$x\^{}7\$ & -\textbackslash(x\^{}7\textbackslash) \\ -2023 & 0.219699 & \$x\^{}8\$ & -\$\textbackslash sin(8x\textbackslash pi/n)\$ & \$x\^{}8\$ & -\textbackslash(x\^{}8\textbackslash) \\ -2024 & 0.861997 & \$x\^{}9\$ & -\$\textbackslash sin(9x\textbackslash pi/n)\$ & \$x\^{}9\$ & -\textbackslash(x\^{}9\textbackslash) \\ - -\end{longtable} - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{sGT(tex, }\StringTok{\textquotesingle{}GT Caption\textquotesingle{}}\NormalTok{)} -\end{Highlighting} -\end{Shaded} - -\begin{table} - -\caption{\label{tbl-tex-2}(Quarto generated caption)} - -\begin{tikzpicture}[ - auto, - transform shape, - nosep/.style={inner sep=0}, - table/.style={ - matrix of nodes, - row sep=0.125em, - column sep=0.375em, - nodes in empty cells, - nodes={rectangle, scale=0.635, text badly ragged }, - row 1/.style={nodes={text=black, anchor=north, inner ysep=0, text height=0, text depth=0}}, - row 2/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}}, - column 1/.style={nodes={align=left }, text height=0.9em, text depth=0.2em, inner xsep=0.375em, inner ysep=0, text width=2.40em}, - column 2/.style={nodes={align=right }, nosep, text width=6.61em}, - column 3/.style={nodes={align=left }, nosep, text width=4.72em}, - column 4/.style={nodes={align=left }, nosep, text width=14.17em}, - column 5/.style={nodes={align=left }, nosep, text width=4.72em}, - column 6/.style={nodes={align=left }, nosep, text width=8.50em}, - column 7/.style={text height=0.9em, text depth=0.2em, nosep, text width=0em} }] -\matrix (TCPW6BX3HRZ2T) [table, ampersand replacement=\&]{ - \& \& \& \& \& \& \\ - x\grtspacer \& A\grtspacer \& B\grtspacer \& $C_1$\grtspacer \& C\_2 not tex\grtspacer \& $\cos(A)$\grtspacer \& \\ - 2020 \& 0.50112 \& $x^5$ \& $\sin(5x\pi/n)$ \& $x^5$ \& \(x^5\) \& \\ - 2021 \& 0.33757 \& $x^6$ \& $\sin(6x\pi/n)$ \& $x^6$ \& \(x^6\) \& \\ - 2022 \& 0.86942 \& $x^7$ \& $\sin(7x\pi/n)$ \& $x^7$ \& \(x^7\) \& \\ - 2023 \& 0.21970 \& $x^8$ \& $\sin(8x\pi/n)$ \& $x^8$ \& \(x^8\) \& \\ - 2024 \& 0.86200 \& $x^9$ \& $\sin(9x\pi/n)$ \& $x^9$ \& \(x^9\) \& \\ -}; - -\path[draw, thick] (TCPW6BX3HRZ2T-1-1.south west) -- (TCPW6BX3HRZ2T-1-7.south east); -\path[draw, semithick] ([yshift=-0.0625em]TCPW6BX3HRZ2T-2-1.south west) -- ([yshift=-0.0625em]TCPW6BX3HRZ2T-2-7.south east); -\path[draw, thick] ([yshift=-0.3125em]TCPW6BX3HRZ2T-7-1.base west) -- ([yshift=-0.3125em]TCPW6BX3HRZ2T-7-7.base east); -\path[draw, very thin] ([xshift=-0.1875em]TCPW6BX3HRZ2T-1-2.south west) -- ([yshift=-0.3125em, xshift=-0.1875em]TCPW6BX3HRZ2T-7-2.base west); - - - -\end{tikzpicture} - -\end{table}% - -Ratio columns. - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{tex.columns }\OperatorTok{=}\NormalTok{ [}\StringTok{"A (\%)"}\NormalTok{, }\StringTok{"B"}\NormalTok{, }\StringTok{"$C\_1$"}\NormalTok{, }\StringTok{"C\_2 not tex"}\NormalTok{, }\StringTok{\textquotesingle{}$}\CharTok{\textbackslash{}\textbackslash{}}\StringTok{cos(A)$\textquotesingle{}}\NormalTok{]} -\NormalTok{sGT(tex, }\StringTok{\textquotesingle{}Ratio columns in A\textquotesingle{}}\NormalTok{, ratio\_cols}\OperatorTok{=}\StringTok{\textquotesingle{}A (\%)\textquotesingle{}}\NormalTok{)} -\end{Highlighting} -\end{Shaded} - -\begin{table} - -\caption{\label{tbl-tex-3}greater table output} - -\begin{tikzpicture}[ - auto, - transform shape, - nosep/.style={inner sep=0}, - table/.style={ - matrix of nodes, - row sep=0.125em, - column sep=0.375em, - nodes in empty cells, - nodes={rectangle, scale=0.635, text badly ragged }, - row 1/.style={nodes={text=black, anchor=north, inner ysep=0, text height=0, text depth=0}}, - row 2/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}}, - column 1/.style={nodes={align=left }, text height=0.9em, text depth=0.2em, inner xsep=0.375em, inner ysep=0, text width=2.40em}, - column 2/.style={nodes={align=right }, nosep, text width=5.67em}, - column 3/.style={nodes={align=left }, nosep, text width=4.72em}, - column 4/.style={nodes={align=left }, nosep, text width=14.17em}, - column 5/.style={nodes={align=left }, nosep, text width=4.72em}, - column 6/.style={nodes={align=left }, nosep, text width=8.50em}, - column 7/.style={text height=0.9em, text depth=0.2em, nosep, text width=0em} }] -\matrix (T5ZEZ3634JGIC) [table, ampersand replacement=\&]{ - \& \& \& \& \& \& \\ - x\grtspacer \& A (\%)\grtspacer \& B\grtspacer \& $C_1$\grtspacer \& C\_2 not tex\grtspacer \& $\cos(A)$\grtspacer \& \\ - 2020 \& 50.1\% \& $x^5$ \& $\sin(5x\pi/n)$ \& $x^5$ \& \(x^5\) \& \\ - 2021 \& 33.8\% \& $x^6$ \& $\sin(6x\pi/n)$ \& $x^6$ \& \(x^6\) \& \\ - 2022 \& 86.9\% \& $x^7$ \& $\sin(7x\pi/n)$ \& $x^7$ \& \(x^7\) \& \\ - 2023 \& 22.0\% \& $x^8$ \& $\sin(8x\pi/n)$ \& $x^8$ \& \(x^8\) \& \\ - 2024 \& 86.2\% \& $x^9$ \& $\sin(9x\pi/n)$ \& $x^9$ \& \(x^9\) \& \\ -}; - -\path[draw, thick] (T5ZEZ3634JGIC-1-1.south west) -- (T5ZEZ3634JGIC-1-7.south east); -\path[draw, semithick] ([yshift=-0.0625em]T5ZEZ3634JGIC-2-1.south west) -- ([yshift=-0.0625em]T5ZEZ3634JGIC-2-7.south east); -\path[draw, thick] ([yshift=-0.3125em]T5ZEZ3634JGIC-7-1.base west) -- ([yshift=-0.3125em]T5ZEZ3634JGIC-7-7.base east); -\path[draw, very thin] ([xshift=-0.1875em]T5ZEZ3634JGIC-1-2.south west) -- ([yshift=-0.3125em, xshift=-0.1875em]T5ZEZ3634JGIC-7-2.base west); - - - -\end{tikzpicture} - -\end{table}% - -\section{Greater\_tables Test Suite}\label{greater_tables-test-suite} - -\phantomsection\label{greater-tables-test} -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{test\_gen }\OperatorTok{=}\NormalTok{ gtu.TestDFGenerator(}\DecValTok{0}\NormalTok{, }\DecValTok{0}\NormalTok{)} -\NormalTok{ans }\OperatorTok{=}\NormalTok{ test\_gen.test\_suite() } -\end{Highlighting} -\end{Shaded} - -\subsection{Test Table: basic}\label{test-table-basic} - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{hrw }\OperatorTok{=}\NormalTok{ (}\DecValTok{0}\NormalTok{, }\DecValTok{0}\NormalTok{, }\DecValTok{0}\NormalTok{)} -\NormalTok{sGT(ans[}\StringTok{\textquotesingle{}basic\textquotesingle{}}\NormalTok{], }\StringTok{"Basic"}\NormalTok{, ratio\_cols}\OperatorTok{=}\StringTok{\textquotesingle{}z\textquotesingle{}}\NormalTok{, aligners}\OperatorTok{=}\NormalTok{\{}\StringTok{\textquotesingle{}w\textquotesingle{}}\NormalTok{: }\StringTok{\textquotesingle{}l\textquotesingle{}}\NormalTok{\},} -\NormalTok{ hrule\_widths}\OperatorTok{=}\NormalTok{hrw)} -\end{Highlighting} -\end{Shaded} - -\begin{table} - -\caption{\label{tbl-greater-tables-test-0}GT output for test table -basic} - -\begin{tikzpicture}[ - auto, - transform shape, - nosep/.style={inner sep=0}, - table/.style={ - matrix of nodes, - row sep=0.125em, - column sep=0.375em, - nodes in empty cells, - nodes={rectangle, scale=0.635, text badly ragged }, - row 1/.style={nodes={text=black, anchor=north, inner ysep=0, text height=0, text depth=0}}, - row 2/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}}, - column 1/.style={nodes={align=left }, text height=0.9em, text depth=0.2em, inner xsep=0.375em, inner ysep=0, text width=3.60em}, - column 2/.style={nodes={align=center}, nosep, text width=6.60em}, - column 3/.style={nodes={align=right }, nosep, text width=6.00em}, - column 4/.style={nodes={align=left }, nosep, text width=8.40em}, - column 5/.style={nodes={align=right }, nosep, text width=4.20em}, - column 6/.style={nodes={align=right }, nosep, text width=5.40em}, - column 7/.style={nodes={align=right }, nosep, text width=9.00em}, - column 8/.style={nodes={align=right }, nosep, text width=10.20em}, - column 9/.style={nodes={align=right }, nosep, text width=6.60em}, - column 10/.style={text height=0.9em, text depth=0.2em, nosep, text width=0em} }] -\matrix (TGBVQTD6WMYO4) [table, ampersand replacement=\&]{ - \& \& \& \& \& \& \& \& \& \\ - unconvinced\grtspacer \& appreciable date\grtspacer \& conception float\grtspacer \& fining str\grtspacer \& hammers float\grtspacer \& molecules float\grtspacer \& ruthlessly float\grtspacer \& sandwiches float\grtspacer \& translating float\grtspacer \& \\ - 8,632 \& 2016-08-13 \& 26.106 \& unsuccessfully \& 0.00402 \& 36.128 \& 63490.304Y \& -906.724y \& 187.654 \& \\ - 8,839 \& 2017-03-18 \& 166.184 \& weighty \& 0.65441 \& 51.906M \& 88.440y \& -0.000y \& 219.176k \& \\ - 10,397 \& 2023-04-12 \& 126.049 \& reinstating \& 0.00435 \& 75.448 \& 158.217E \& -1.141Y \& 6.696M \& \\ - 19,251 \& 2031-02-20 \& 9.514M \& regularly \& 0.00013 \& 1.919 \& 53.921P \& 456.467f \& 980.398 \& \\ - 35,202 \& 2022-01-29 \& 12.016M \& downplayed \& 0.00001 \& 4.675G \& 66.313a \& -2.355y \& 450.111m \& \\ - 46,310 \& 2017-03-18 \& 1.785G \& harmful \& 0.00392 \& 88.559 \& -98.569P \& 128.613n \& 142.900 \& \\ - 55,986 \& 2031-02-20 \& 39.829 \& paradise \& 0.00000 \& 4.541M \& 752.248M \& 8.739E \& 254.917k \& \\ - 61,765 \& 2016-08-13 \& 46.325M \& diagrams \& 4.36743 \& 11.110k \& 18790.418Y \& 310.420E \& 200.569 \& \\ - 79,238 \& 2030-11-17 \& 13.733M \& shortfall \& 0.00000 \& 34.625 \& -550909914.756Y \& -63486983222.994Y \& 23.893M \& \\ - 92,160 \& 2023-04-12 \& 3.877 \& composers \& 0.00002 \& 57.548 \& 111.540p \& -2.330Y \& 3.200G \& \\ -}; - -\path[draw, thick] (TGBVQTD6WMYO4-1-1.south west) -- (TGBVQTD6WMYO4-1-10.south east); -\path[draw, semithick] ([yshift=-0.0625em]TGBVQTD6WMYO4-2-1.south west) -- ([yshift=-0.0625em]TGBVQTD6WMYO4-2-10.south east); -\path[draw, thick] ([yshift=-0.3125em]TGBVQTD6WMYO4-12-1.base west) -- ([yshift=-0.3125em]TGBVQTD6WMYO4-12-10.base east); -\path[draw, very thin] ([xshift=-0.1875em]TGBVQTD6WMYO4-1-2.south west) -- ([yshift=-0.3125em, xshift=-0.1875em]TGBVQTD6WMYO4-12-2.base west); - - - -\end{tikzpicture} - -\end{table}% - -Comments go here. - -\subsection{Test Table: timeseries}\label{test-table-timeseries} - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{hrw }\OperatorTok{=}\NormalTok{ (}\DecValTok{0}\NormalTok{, }\DecValTok{0}\NormalTok{, }\DecValTok{0}\NormalTok{)} -\NormalTok{sGT(ans[}\StringTok{\textquotesingle{}timeseries\textquotesingle{}}\NormalTok{], }\StringTok{"Timeseries"}\NormalTok{, ratio\_cols}\OperatorTok{=}\StringTok{\textquotesingle{}z\textquotesingle{}}\NormalTok{, aligners}\OperatorTok{=}\NormalTok{\{}\StringTok{\textquotesingle{}w\textquotesingle{}}\NormalTok{: }\StringTok{\textquotesingle{}l\textquotesingle{}}\NormalTok{\},} -\NormalTok{ hrule\_widths}\OperatorTok{=}\NormalTok{hrw)} -\end{Highlighting} -\end{Shaded} - -\begin{table} - -\caption{\label{tbl-greater-tables-test-1}GT output for test table -timeseries} - -\begin{tikzpicture}[ - auto, - transform shape, - nosep/.style={inner sep=0}, - table/.style={ - matrix of nodes, - row sep=0.125em, - column sep=0.375em, - nodes in empty cells, - nodes={rectangle, scale=0.635, text badly ragged }, - row 1/.style={nodes={text=black, anchor=north, inner ysep=0, text height=0, text depth=0}}, - row 2/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}}, - column 1/.style={nodes={align=left }, text height=0.9em, text depth=0.2em, inner xsep=0.375em, inner ysep=0, text width=6.00em}, - column 2/.style={nodes={align=right }, nosep, text width=9.45em}, - column 3/.style={nodes={align=center}, nosep, text width=9.45em}, - column 4/.style={nodes={align=center}, nosep, text width=9.45em}, - column 5/.style={text height=0.9em, text depth=0.2em, nosep, text width=0em} }] -\matrix (TBSYLUFCI4LBB) [table, ampersand replacement=\&]{ - \& \& \& \& \\ - bemoan\grtspacer \& Absolute Affirmed Mutton float\grtspacer \& Adjourns Evaluation Dismantling datetime\grtspacer \& Hispanic Prohibit Skeptical datetime\grtspacer \& \\ - 2011-01-09 \& -0.000y \& 2026-02-13 \& 2025-07-20 \& \\ - 2012-01-09 \& -2.716a \& 2011-10-23 \& 2018-05-10 \& \\ - 2012-03-01 \& 291.376Z \& 2014-05-17 \& 2031-10-23 \& \\ - 2012-03-27 \& 2.489P \& 2030-10-30 \& 2007-08-24 \& \\ - 2014-01-07 \& 957.797M \& 2012-11-22 \& 2025-07-20 \& \\ - 2015-08-18 \& -25.750 \& 2024-10-01 \& 2025-06-29 \& \\ - 2015-12-13 \& -81.647p \& 2028-04-20 \& 2020-01-17 \& \\ - 2016-06-01 \& 0.000y \& 2009-06-25 \& 2020-01-17 \& \\ - 2018-03-06 \& 0.000y \& 2012-09-29 \& 2018-09-28 \& \\ - 2019-03-05 \& -3.510p \& 2030-06-13 \& 2008-01-30 \& \\ - 2019-03-09 \& 1.662u \& 2012-11-22 \& 2025-06-29 \& \\ - 2020-11-02 \& 99.120P \& 2009-06-25 \& 2029-07-27 \& \\ - 2020-11-20 \& 0.232y \& 2016-09-29 \& 2007-05-27 \& \\ - 2020-12-08 \& 29.010a \& 2006-09-15 \& 2032-04-04 \& \\ - 2021-07-30 \& -398.788u \& 2011-10-23 \& 2032-04-04 \& \\ - 2021-09-25 \& 3.780y \& 2029-02-24 \& 2007-04-22 \& \\ - 2021-11-27 \& 0.000y \& 2026-02-13 \& 2018-09-28 \& \\ - 2027-03-28 \& -85.745E \& 2015-10-22 \& 2032-03-19 \& \\ - 2029-05-28 \& 57.186k \& 2015-08-12 \& 2008-01-30 \& \\ - 2033-02-27 \& -496.810f \& 2024-10-01 \& 2032-04-04 \& \\ -}; - -\path[draw, thick] (TBSYLUFCI4LBB-1-1.south west) -- (TBSYLUFCI4LBB-1-5.south east); -\path[draw, semithick] ([yshift=-0.0625em]TBSYLUFCI4LBB-2-1.south west) -- ([yshift=-0.0625em]TBSYLUFCI4LBB-2-5.south east); -\path[draw, thick] ([yshift=-0.3125em]TBSYLUFCI4LBB-22-1.base west) -- ([yshift=-0.3125em]TBSYLUFCI4LBB-22-5.base east); -\path[draw, very thin] ([xshift=-0.1875em]TBSYLUFCI4LBB-1-2.south west) -- ([yshift=-0.3125em, xshift=-0.1875em]TBSYLUFCI4LBB-22-2.base west); - - - -\end{tikzpicture} - -\end{table}% - -Comments go here. - -\subsection{Test Table: multiindex}\label{test-table-multiindex} - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{hrw }\OperatorTok{=}\NormalTok{ (}\FloatTok{1.5}\NormalTok{, }\FloatTok{1.0}\NormalTok{, }\FloatTok{0.5}\NormalTok{)} -\NormalTok{sGT(ans[}\StringTok{\textquotesingle{}multiindex\textquotesingle{}}\NormalTok{], }\StringTok{"Multiindex"}\NormalTok{, ratio\_cols}\OperatorTok{=}\StringTok{\textquotesingle{}z\textquotesingle{}}\NormalTok{, aligners}\OperatorTok{=}\NormalTok{\{}\StringTok{\textquotesingle{}w\textquotesingle{}}\NormalTok{: }\StringTok{\textquotesingle{}l\textquotesingle{}}\NormalTok{\},} -\NormalTok{ hrule\_widths}\OperatorTok{=}\NormalTok{hrw)} -\end{Highlighting} -\end{Shaded} - -\begin{table} - -\caption{\label{tbl-greater-tables-test-2}GT output for test table -multiindex} - -\begin{tikzpicture}[ - auto, - transform shape, - nosep/.style={inner sep=0}, - table/.style={ - matrix of nodes, - row sep=0.125em, - column sep=0.375em, - nodes in empty cells, - nodes={rectangle, scale=0.635, text badly ragged }, - row 1/.style={nodes={text=black, anchor=north, inner ysep=0, text height=0, text depth=0}}, - row 2/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}}, - column 1/.style={nodes={align=left }, text height=0.9em, text depth=0.2em, inner xsep=0.375em, inner ysep=0, text width=3.60em}, - column 2/.style={nodes={align=left }, nosep, text width=6.00em}, - column 3/.style={nodes={align=left }, nosep, text width=3.60em}, - column 4/.style={nodes={align=right }, nosep, text width=7.71em}, - column 5/.style={nodes={align=right }, nosep, text width=8.48em}, - column 6/.style={nodes={align=right }, nosep, text width=10.02em}, - column 7/.style={nodes={align=right }, nosep, text width=9.25em}, - column 8/.style={nodes={align=right }, nosep, text width=8.48em}, - column 9/.style={text height=0.9em, text depth=0.2em, nosep, text width=0em} }] -\matrix (TPDCP6TYBOZMN) [table, ampersand replacement=\&]{ - \& \& \& \& \& \& \& \& \\ - reactions\grtspacer \& belligerent\grtspacer \& inaugural\grtspacer \& Action Formulates Succeeded float\grtspacer \& Designate Vestige Reservation float\grtspacer \& Distinguishes Investments Contemplates year\grtspacer \& Hesitate Premiere Conspiracies year\grtspacer \& Newark Waved Impoverish int\grtspacer \& \\ - 10,971 \& invaluable \& 34,061 \& -6.471u \& 808.075k \& 2027 \& 2012 \& 901,426,869 \& \\ - \& invaluable \& 43,523 \& 18.077u \& 3.209G \& 2027 \& 2010 \& 521,984,844 \& \\ - \& malevolent \& 75,221 \& -845.354u \& 128.915m \& 1995 \& 2005 \& 434,046,672 \& \\ - \& saddens \& 39,194 \& 36.518z \& 3.945M \& 1996 \& 2019 \& 755,593,582 \& \\ - \& saddens \& 56,895 \& 22.781u \& 22.434M \& 2000 \& 1999 \& 510,854,557 \& \\ - \& saddens \& 64,039 \& 0.254y \& 368.327 \& 2022 \& 2005 \& 313,805,927 \& \\ - \& saddens \& 87,079 \& 3.120a \& 18.891M \& 1992 \& 1996 \& 74,515,255 \& \\ - 98,173 \& invaluable \& 49,891 \& 1.454n \& 1.702k \& 1996 \& 2004 \& 884,473,151 \& \\ - \& malevolent \& 24,303 \& -486.778Y \& 680.242 \& 2024 \& 2006 \& 223,313,250 \& \\ - \& malevolent \& 40,740 \& -0.000y \& 77.347M \& 2021 \& 2000 \& 888,657,488 \& \\ -}; - -\path[draw, thick] (TPDCP6TYBOZMN-1-1.south west) -- (TPDCP6TYBOZMN-1-9.south east); -\path[draw, very thin] ([yshift=-0.0625em]TPDCP6TYBOZMN-9-1.south west) -- ([yshift=-0.0625em]TPDCP6TYBOZMN-9-9.south east); -\path[draw, semithick] ([yshift=-0.0625em]TPDCP6TYBOZMN-2-1.south west) -- ([yshift=-0.0625em]TPDCP6TYBOZMN-2-9.south east); -\path[draw, thick] ([yshift=-0.3125em]TPDCP6TYBOZMN-12-1.base west) -- ([yshift=-0.3125em]TPDCP6TYBOZMN-12-9.base east); -\path[draw, very thin] ([xshift=-0.1875em]TPDCP6TYBOZMN-1-4.south west) -- ([yshift=-0.3125em, xshift=-0.1875em]TPDCP6TYBOZMN-12-4.base west); - - - -\end{tikzpicture} - -\end{table}% - -Comments go here. - -\subsection{Test Table: multicolumns}\label{test-table-multicolumns} - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{hrw }\OperatorTok{=}\NormalTok{ (}\DecValTok{0}\NormalTok{, }\DecValTok{0}\NormalTok{, }\DecValTok{0}\NormalTok{)} -\NormalTok{sGT(ans[}\StringTok{\textquotesingle{}multicolumns\textquotesingle{}}\NormalTok{], }\StringTok{"Multicolumns"}\NormalTok{, ratio\_cols}\OperatorTok{=}\StringTok{\textquotesingle{}z\textquotesingle{}}\NormalTok{, aligners}\OperatorTok{=}\NormalTok{\{}\StringTok{\textquotesingle{}w\textquotesingle{}}\NormalTok{: }\StringTok{\textquotesingle{}l\textquotesingle{}}\NormalTok{\},} -\NormalTok{ hrule\_widths}\OperatorTok{=}\NormalTok{hrw)} -\end{Highlighting} -\end{Shaded} - -\begin{table} - -\caption{\label{tbl-greater-tables-test-3}GT output for test table -multicolumns} - -\begin{tikzpicture}[ - auto, - transform shape, - nosep/.style={inner sep=0}, - table/.style={ - matrix of nodes, - row sep=0.125em, - column sep=0.375em, - nodes in empty cells, - nodes={rectangle, scale=0.635, text badly ragged }, - row 1/.style={nodes={text=black, anchor=north, inner ysep=0, text height=0, text depth=0}}, - row 2/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}}, - row 3/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}}, - row 4/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}}, - column 1/.style={nodes={align=left }, text height=0.9em, text depth=0.2em, inner xsep=0.375em, inner ysep=0, text width=4.20em}, - column 2/.style={nodes={align=left }, nosep, text width=11.28em}, - column 3/.style={nodes={align=right }, nosep, text width=11.28em}, - column 4/.style={nodes={align=right }, nosep, text width=9.55em}, - column 5/.style={nodes={align=left }, nosep, text width=10.42em}, - column 6/.style={nodes={align=right }, nosep, text width=10.42em}, - column 7/.style={text height=0.9em, text depth=0.2em, nosep, text width=0em} }] -\matrix (TNTJBCNKN57RB) [table, ampersand replacement=\&]{ - \& \& \& \& \& \& \\ - \grtspacer \& repetitive\grtspacer \& \grtspacer \& \grtspacer \& tutu\grtspacer \& \grtspacer \& \\ - \grtspacer \& bicker\grtspacer \& wishes\grtspacer \& \grtspacer \& assimilation\grtspacer \& \grtspacer \& \\ - lecture\grtspacer \& addresses\grtspacer \& accommodating\grtspacer \& registrants\grtspacer \& cadres\grtspacer \& lectures\grtspacer \& \\ - 4,873 \& hack \& 2023 \& 3,089 \& undercurrent \& 1996 \& \\ - 31,679 \& stabbing \& 2018 \& 6,871 \& episode \& 2017 \& \\ - 38,283 \& awarded \& 2018 \& -7,895 \& turner \& 2019 \& \\ - 40,641 \& accord \& 2007 \& -3,597 \& rattling \& 2017 \& \\ - 44,030 \& corroborating \& 2021 \& -9,395 \& relaunch \& 2010 \& \\ - 59,729 \& digest \& 1993 \& 298 \& fixate \& 2020 \& \\ - 65,534 \& deader \& 2011 \& -9,990 \& escalation \& 2029 \& \\ - 86,783 \& arrows \& 2015 \& -535 \& rebellion \& 2026 \& \\ - 89,904 \& refinery \& 1994 \& -3,027 \& vacant \& 1993 \& \\ - 92,799 \& affirmation \& 1995 \& -7,911 \& hobby \& 2003 \& \\ -}; - -\path[draw, thick] (TNTJBCNKN57RB-1-1.south west) -- (TNTJBCNKN57RB-1-7.south east); -\path[draw, semithick] ([yshift=-0.0625em]TNTJBCNKN57RB-4-1.south west) -- ([yshift=-0.0625em]TNTJBCNKN57RB-4-7.south east); -\path[draw, thick] ([yshift=-0.3125em]TNTJBCNKN57RB-14-1.base west) -- ([yshift=-0.3125em]TNTJBCNKN57RB-14-7.base east); -\path[draw, very thin] ([xshift=-0.1875em, yshift=-0.0625em]TNTJBCNKN57RB-2-2.south west) -- ([yshift=-0.0625em]TNTJBCNKN57RB-2-7.south east); -\path[draw, very thin] ([xshift=-0.1875em, yshift=-0.0625em]TNTJBCNKN57RB-3-2.south west) -- ([yshift=-0.0625em]TNTJBCNKN57RB-3-7.south east); -\path[draw, very thin] ([xshift=-0.1875em]TNTJBCNKN57RB-1-2.south west) -- ([yshift=-0.3125em, xshift=-0.1875em]TNTJBCNKN57RB-14-2.base west); -\path[draw, ultra thin] ([xshift=0.1875em, yshift=-0.0625em]TNTJBCNKN57RB-1-4.south east) -- ([yshift=-0.3125em, xshift=0.1875em]TNTJBCNKN57RB-14-4.base east); -\path[draw, ultra thin] ([xshift=0.1875em, yshift=-0.0625em]TNTJBCNKN57RB-2-2.south east) -- ([yshift=-0.3125em, xshift=0.1875em]TNTJBCNKN57RB-14-2.base east); - - - -\end{tikzpicture} - -\end{table}% - -Comments go here. - -\subsection{Test Table: complex}\label{test-table-complex} - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{hrw }\OperatorTok{=}\NormalTok{ (}\FloatTok{1.5}\NormalTok{, }\FloatTok{1.0}\NormalTok{, }\FloatTok{0.5}\NormalTok{)} -\NormalTok{sGT(ans[}\StringTok{\textquotesingle{}complex\textquotesingle{}}\NormalTok{], }\StringTok{"Complex"}\NormalTok{, ratio\_cols}\OperatorTok{=}\StringTok{\textquotesingle{}z\textquotesingle{}}\NormalTok{, aligners}\OperatorTok{=}\NormalTok{\{}\StringTok{\textquotesingle{}w\textquotesingle{}}\NormalTok{: }\StringTok{\textquotesingle{}l\textquotesingle{}}\NormalTok{\},} -\NormalTok{ hrule\_widths}\OperatorTok{=}\NormalTok{hrw)} -\end{Highlighting} -\end{Shaded} - -\begin{table} - -\caption{\label{tbl-greater-tables-test-4}GT output for test table -complex} - -\begin{tikzpicture}[ - auto, - transform shape, - nosep/.style={inner sep=0}, - table/.style={ - matrix of nodes, - row sep=0.125em, - column sep=0.375em, - nodes in empty cells, - nodes={rectangle, scale=0.635, text badly ragged }, - row 1/.style={nodes={text=black, anchor=north, inner ysep=0, text height=0, text depth=0}}, - row 2/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}}, - row 3/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}}, - row 4/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}}, - column 1/.style={nodes={align=left }, text height=0.9em, text depth=0.2em, inner xsep=0.375em, inner ysep=0, text width=3.60em}, - column 2/.style={nodes={align=left }, nosep, text width=7.20em}, - column 3/.style={nodes={align=left }, nosep, text width=6.00em}, - column 4/.style={nodes={align=left }, nosep, text width=7.20em}, - column 5/.style={nodes={align=right }, nosep, text width=7.20em}, - column 6/.style={nodes={align=right }, nosep, text width=7.20em}, - column 7/.style={nodes={align=right }, nosep, text width=7.20em}, - column 8/.style={nodes={align=right }, nosep, text width=12.00em}, - column 9/.style={nodes={align=center}, nosep, text width=6.60em}, - column 10/.style={nodes={align=center}, nosep, text width=7.20em}, - column 11/.style={nodes={align=right }, nosep, text width=6.60em}, - column 12/.style={nodes={align=left }, nosep, text width=7.80em}, - column 13/.style={nodes={align=left }, nosep, text width=7.20em}, - column 14/.style={text height=0.9em, text depth=0.2em, nosep, text width=0em} }] -\matrix (TYKTNDZBEDOSG) [table, ampersand replacement=\&]{ - \& \& \& \& \& \& \& \& \& \& \& \& \& \\ - \grtspacer \& \grtspacer \& \grtspacer \& diagrammatic\grtspacer \& \grtspacer \& \grtspacer \& \grtspacer \& \grtspacer \& intensely\grtspacer \& \grtspacer \& \grtspacer \& \grtspacer \& \grtspacer \& \\ - \grtspacer \& \grtspacer \& \grtspacer \& correlation\grtspacer \& \grtspacer \& \grtspacer \& william\grtspacer \& \grtspacer \& cardiac\grtspacer \& william\grtspacer \& \grtspacer \& \grtspacer \& \grtspacer \& \\ - sermon\grtspacer \& idle\grtspacer \& librarians\grtspacer \& express\grtspacer \& neighbor\grtspacer \& unmistakable\grtspacer \& connectivity\grtspacer \& obscures\grtspacer \& demographic\grtspacer \& manufacturer\grtspacer \& outlaws\grtspacer \& pulled\grtspacer \& wireless\grtspacer \& \\ - 51,701 \& better \& 40,112 \& innumerable \& 48.980M \& 4,249 \& 128.796m \& 6.663z \& 2011-08-25 \& 2026-01-16 \& 869,081,663 \& providers \& briefing \& \\ - \& complicated \& 3,926 \& pentecostal \& 59.707 \& -825 \& 8.145G \& 15.501E \& 2026-07-20 \& 2014-12-05 \& 202,632,105 \& hamster \& goth \& \\ - \& complicated \& 12,208 \& proportions \& 18.027k \& 8,008 \& 2.001G \& 18.602Y \& 2011-08-25 \& 2016-07-03 \& 510,388,466 \& girlfriends \& mythology \& \\ - \& complicated \& 65,629 \& navigated \& 11.940k \& 6,378 \& 48.117 \& -113.851u \& 2026-07-20 \& 2030-10-01 \& 395,706,791 \& qualification \& adequate \& \\ - \& methodically \& 27,349 \& sawmill \& 4.033k \& 8,090 \& 361.908m \& 12076296027110.290Y \& 2028-08-07 \& 2007-08-27 \& 75,711,684 \& behaviors \& timing \& \\ - \& methodically \& 43,485 \& parentheses \& 9.546 \& -1,250 \& 1.301G \& -143231.502Y \& 2018-12-09 \& 2008-11-29 \& 954,513,855 \& figure \& telescopic \& \\ - \& methodically \& 55,700 \& forgive \& 2.792G \& 2,953 \& 3.292M \& 255.417z \& 2031-12-19 \& 2008-11-25 \& 172,715,663 \& distant \& hobby \& \\ - \& methodically \& 60,105 \& consultants \& 172.060 \& -5,666 \& 5.968k \& -21.254a \& 2026-07-20 \& 2030-10-01 \& 449,538,011 \& unloaded \& munchies \& \\ - \& methodically \& 98,580 \& mandating \& 74.624k \& 5,684 \& 8.510M \& -0.000y \& 2026-06-26 \& 2021-09-12 \& 988,320,370 \& monochrome \& rebuilt \& \\ - 99,724 \& better \& 6,020 \& broached \& 3.282k \& 8,757 \& 1.264G \& 494216364.082Y \& 2016-05-06 \& 2008-11-25 \& 582,779,298 \& discriminates \& bestowed \& \\ - \& better \& 15,116 \& parallel \& 126.036M \& 4,638 \& 715.691M \& -6084.833Y \& 2031-09-06 \& 2014-12-05 \& 276,261,271 \& precisely \& handily \& \\ - \& better \& 24,824 \& lifesaver \& 53.513 \& -8,038 \& 7.370G \& -13.689Y \& 2011-08-25 \& 2033-06-20 \& 643,278,224 \& masthead \& pakistani \& \\ - \& better \& 65,455 \& fidelity \& 471.271M \& 8,256 \& 3.143k \& -64054884217.656Y \& 2011-08-25 \& 2033-06-20 \& 99,430,099 \& storyboard \& buddies \& \\ - \& better \& 81,893 \& accumulating \& 13.893M \& 7,426 \& 105.856 \& 0.000y \& 2018-12-04 \& 2009-11-22 \& 223,246,972 \& murderers \& cooperating \& \\ - \& complicated \& 2,248 \& covering \& 202.243m \& -5,336 \& 225.260M \& 93.754n \& 2011-12-27 \& 2026-01-29 \& 225,832,976 \& seizes \& concluding \& \\ - \& complicated \& 51,296 \& golden \& 9.341M \& -8,036 \& 142.880 \& -537.634M \& 2018-12-04 \& 2021-09-12 \& 199,792,598 \& moons \& lark \& \\ - \& complicated \& 54,923 \& eventuality \& 3.545k \& 595 \& 166.334 \& -1.033Z \& 2026-06-26 \& 2015-07-20 \& 440,990,498 \& egghead \& wreaks \& \\ - \& methodically \& 7,550 \& waters \& 437.510k \& -1,867 \& 24.289k \& -0.000y \& 2026-07-20 \& 2019-06-07 \& 389,874,646 \& voicing \& boeing \& \\ - \& methodically \& 83,418 \& blankets \& 9.726G \& -4,364 \& 763.757k \& 3.599k \& 2011-08-25 \& 2026-01-02 \& 640,410,908 \& whittle \& abbreviation \& \\ - \& methodically \& 98,887 \& accompany \& 1.831M \& 1,106 \& 2.931k \& -629013.362Y \& 2014-01-02 \& 2007-08-27 \& 855,249,101 \& bigwigs \& portfolio \& \\ -}; - -\path[draw, thick] (TYKTNDZBEDOSG-1-1.south west) -- (TYKTNDZBEDOSG-1-14.south east); -\path[draw, thick] ([yshift=-0.3125em]TYKTNDZBEDOSG-24-1.base west) -- ([yshift=-0.3125em]TYKTNDZBEDOSG-24-14.base east); -\path[draw, semithick] ([yshift=-0.0625em]TYKTNDZBEDOSG-4-1.south west) -- ([yshift=-0.0625em]TYKTNDZBEDOSG-4-14.south east); -\path[draw, very thin] ([yshift=-0.0625em]TYKTNDZBEDOSG-13-1.south west) -- ([yshift=-0.0625em]TYKTNDZBEDOSG-13-14.south east); -\path[draw, very thin] ([xshift=-0.1875em, yshift=-0.0625em]TYKTNDZBEDOSG-2-4.south west) -- ([yshift=-0.0625em]TYKTNDZBEDOSG-2-14.south east); -\path[draw, very thin] ([xshift=-0.1875em, yshift=-0.0625em]TYKTNDZBEDOSG-3-4.south west) -- ([yshift=-0.0625em]TYKTNDZBEDOSG-3-14.south east); -\path[draw, very thin] ([xshift=-0.1875em]TYKTNDZBEDOSG-1-4.south west) -- ([yshift=-0.3125em, xshift=-0.1875em]TYKTNDZBEDOSG-24-4.base west); -\path[draw, ultra thin] ([xshift=0.1875em, yshift=-0.0625em]TYKTNDZBEDOSG-1-8.south east) -- ([yshift=-0.3125em, xshift=0.1875em]TYKTNDZBEDOSG-24-8.base east); -\path[draw, ultra thin] ([xshift=0.1875em, yshift=-0.0625em]TYKTNDZBEDOSG-2-6.south east) -- ([yshift=-0.3125em, xshift=0.1875em]TYKTNDZBEDOSG-24-6.base east); -\path[draw, ultra thin] ([xshift=0.1875em, yshift=-0.0625em]TYKTNDZBEDOSG-2-9.south east) -- ([yshift=-0.3125em, xshift=0.1875em]TYKTNDZBEDOSG-24-9.base east); - - - -\end{tikzpicture} - -\end{table}% - -Comments go here. - -\section{Other input formats}\label{other-input-formats} - -\subsection{Markown}\label{markown} - -\begin{longtable}[]{@{} - >{\raggedright\arraybackslash}p{(\linewidth - 6\tabcolsep) * \real{0.7093}} - >{\centering\arraybackslash}p{(\linewidth - 6\tabcolsep) * \real{0.1047}} - >{\centering\arraybackslash}p{(\linewidth - 6\tabcolsep) * \real{0.0930}} - >{\centering\arraybackslash}p{(\linewidth - 6\tabcolsep) * \real{0.0930}}@{}} -\toprule\noalign{} -\begin{minipage}[b]{\linewidth}\raggedright -\textbf{Insured group or insurance product} -\end{minipage} & \begin{minipage}[b]{\linewidth}\centering -\textbf{Sat} -\end{minipage} & \begin{minipage}[b]{\linewidth}\centering -\textbf{RP} -\end{minipage} & \begin{minipage}[b]{\linewidth}\centering -\textbf{RF} -\end{minipage} \\ -\midrule\noalign{} -\endhead -\bottomrule\noalign{} -\endlastfoot -Non-standard auto & x & & \\ -General liability for judgment proof corporation & x & & \\ -Term life insurance & & x & \\ -Catastrophe Reinsurance, outside rating agency bounds & & x & \\ -High limit property per risk reinsurance & & x & \\ -Personal lines for affluent individuals & x & x & \\ -Small commercial lines & x & x & \\ -Catastrophe reinsurance, within rating agency bounds & x & x & \\ -Large account captive reinsurance & & & x \\ -Structured quota share, requiring a risk transfer test & x & & x \\ -Working layer casualty excess of loss & & x & x \\ -Surplus relief quota share on cat exposed line & x & x & x \\ -Middle market commercial lines work comp or commercial auto & x & x & -x \\ -\end{longtable} - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{txt }\OperatorTok{=} \StringTok{\textquotesingle{}\textquotesingle{}\textquotesingle{}} - -\StringTok{| **Insured group or insurance product** | **Sat** | **RP** | **RF** |} -\StringTok{|:{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}|:{-}{-}{-}{-}{-}{-}{-}:|:{-}{-}{-}{-}{-}{-}:|:{-}{-}{-}{-}{-}{-}:|} -\StringTok{| Non{-}standard auto | x | | |} -\StringTok{| General liability for judgment proof corporation | x | | |} -\StringTok{| Term life insurance | | x | |} -\StringTok{| Catastrophe Reinsurance, outside rating agency bounds | | x | |} -\StringTok{| High limit property per risk reinsurance | | x | |} -\StringTok{| Personal lines for affluent individuals | x | x | |} -\StringTok{| Small commercial lines | x | x | |} -\StringTok{| Catastrophe reinsurance, within rating agency bounds | x | x | |} -\StringTok{| Large account captive reinsurance | | | x |} -\StringTok{| Structured quota share, requiring a risk transfer test | x | | x |} -\StringTok{| Working layer casualty excess of loss | | x | x |} -\StringTok{| Surplus relief quota share on cat exposed line | x | x | x |} -\StringTok{| Middle market commercial lines work comp or commercial auto | x | x | x |} - - -\StringTok{\textquotesingle{}\textquotesingle{}\textquotesingle{}} - -\NormalTok{GT(txt)} -\end{Highlighting} -\end{Shaded} - -\begin{table} - -\caption{\label{tbl-greater-tables-test-5}GT from markdown table input} - -\begin{tikzpicture}[ - auto, - transform shape, - nosep/.style={inner sep=0}, - table/.style={ - matrix of nodes, - row sep=0.125em, - column sep=0.375em, - nodes in empty cells, - nodes={rectangle, scale=0.635, text badly ragged }, - row 1/.style={nodes={text=black, anchor=north, inner ysep=0, text height=0, text depth=0}}, - row 2/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}}, - column 1/.style={nodes={align=left }, text height=0.9em, text depth=0.2em, inner xsep=0.375em, inner ysep=0, text width=51.09em}, - column 2/.style={nodes={align=center}, nosep, text width=2.60em}, - column 3/.style={nodes={align=center}, nosep, text width=2.00em}, - column 4/.style={nodes={align=center}, nosep, text width=2.00em}, - column 5/.style={text height=0.9em, text depth=0.2em, nosep, text width=0em} }] -\matrix (TEQZIBDCCW47A) [table, ampersand replacement=\&]{ - \& \& \& \& \\ - Insured group or insurance product\grtspacer \& Sat\grtspacer \& RP\grtspacer \& RF\grtspacer \& \\ - Non-standard auto \& x \& \& \& \\ - General liability for judgment proof corporation \& x \& \& \& \\ - Term life insurance \& \& x \& \& \\ - Catastrophe Reinsurance, outside rating agency bounds \& \& x \& \& \\ - High limit property per risk reinsurance \& \& x \& \& \\ - Personal lines for affluent individuals \& x \& x \& \& \\ - Small commercial lines \& x \& x \& \& \\ - Catastrophe reinsurance, within rating agency bounds \& x \& x \& \& \\ - Large account captive reinsurance \& \& \& x \& \\ - Structured quota share, requiring a risk transfer test \& x \& \& x \& \\ - Working layer casualty excess of loss \& \& x \& x \& \\ - Surplus relief quota share on cat exposed line \& x \& x \& x \& \\ - Middle market commercial lines work comp or commercial auto \& x \& x \& x \& \\ -}; - -\path[draw, thick] (TEQZIBDCCW47A-1-1.south west) -- (TEQZIBDCCW47A-1-5.south east); -\path[draw, semithick] ([yshift=-0.0625em]TEQZIBDCCW47A-2-1.south west) -- ([yshift=-0.0625em]TEQZIBDCCW47A-2-5.south east); -\path[draw, thick] ([yshift=-0.3125em]TEQZIBDCCW47A-15-1.base west) -- ([yshift=-0.3125em]TEQZIBDCCW47A-15-5.base east); -\path[draw, very thin] ([xshift=-0.1875em]TEQZIBDCCW47A-1-1.south west) -- ([yshift=-0.3125em, xshift=-0.1875em]TEQZIBDCCW47A-15-1.base west); - - - -\end{tikzpicture} - -\end{table}% - -\subsection{List of lists}\label{list-of-lists} - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{lol }\OperatorTok{=}\NormalTok{ [[}\StringTok{\textquotesingle{}a\textquotesingle{}}\NormalTok{, }\StringTok{\textquotesingle{}b\textquotesingle{}}\NormalTok{, }\StringTok{\textquotesingle{}c\textquotesingle{}}\NormalTok{, }\StringTok{\textquotesingle{}d\textquotesingle{}}\NormalTok{], [}\StringTok{\textquotesingle{}west\textquotesingle{}}\NormalTok{, }\DecValTok{10}\NormalTok{, }\DecValTok{20}\NormalTok{, }\DecValTok{30}\NormalTok{], [}\StringTok{\textquotesingle{}east\textquotesingle{}}\NormalTok{, }\DecValTok{10}\NormalTok{, }\DecValTok{200}\NormalTok{, }\DecValTok{30}\NormalTok{], [}\StringTok{\textquotesingle{}north\textquotesingle{}}\NormalTok{, }\DecValTok{10}\NormalTok{, }\DecValTok{20}\NormalTok{, }\DecValTok{300}\NormalTok{], [}\StringTok{\textquotesingle{}south\textquotesingle{}}\NormalTok{, }\DecValTok{100}\NormalTok{, }\DecValTok{20}\NormalTok{, }\DecValTok{30}\NormalTok{]]} -\NormalTok{GT(lol)} -\end{Highlighting} -\end{Shaded} - -\begin{table} - -\caption{\label{tbl-greater-tables-test-6}GT output for list of lists -input} - -\begin{tikzpicture}[ - auto, - transform shape, - nosep/.style={inner sep=0}, - table/.style={ - matrix of nodes, - row sep=0.125em, - column sep=0.375em, - nodes in empty cells, - nodes={rectangle, scale=0.635, text badly ragged }, - row 1/.style={nodes={text=black, anchor=north, inner ysep=0, text height=0, text depth=0}}, - row 2/.style={nodes={text=black, anchor=south, inner ysep=.2em, minimum height=1.3em, font=\bfseries}}, - column 1/.style={nodes={align=left }, text height=0.9em, text depth=0.2em, inner xsep=0.375em, inner ysep=0, text width=4.72em}, - column 2/.style={nodes={align=left }, nosep, text width=2.83em}, - column 3/.style={nodes={align=left }, nosep, text width=2.83em}, - column 4/.style={nodes={align=left }, nosep, text width=2.83em}, - column 5/.style={text height=0.9em, text depth=0.2em, nosep, text width=0em} }] -\matrix (T4XHJ53EN656B) [table, ampersand replacement=\&]{ - \& \& \& \& \\ - a\grtspacer \& b\grtspacer \& c\grtspacer \& d\grtspacer \& \\ - west \& 10 \& 20 \& 30 \& \\ - east \& 10 \& 200 \& 30 \& \\ - north \& 10 \& 20 \& 300 \& \\ - south \& 100 \& 20 \& 30 \& \\ -}; - -\path[draw, thick] (T4XHJ53EN656B-1-1.south west) -- (T4XHJ53EN656B-1-5.south east); -\path[draw, semithick] ([yshift=-0.0625em]T4XHJ53EN656B-2-1.south west) -- ([yshift=-0.0625em]T4XHJ53EN656B-2-5.south east); -\path[draw, thick] ([yshift=-0.3125em]T4XHJ53EN656B-6-1.base west) -- ([yshift=-0.3125em]T4XHJ53EN656B-6-5.base east); -\path[draw, very thin] ([xshift=-0.1875em]T4XHJ53EN656B-1-1.south west) -- ([yshift=-0.3125em, xshift=-0.1875em]T4XHJ53EN656B-6-1.base west); - - - -\end{tikzpicture} - -\end{table}% - - - - -\end{document} diff --git a/tests/test_tables.py b/tests/test_tables.py deleted file mode 100644 index ef42cb0..0000000 --- a/tests/test_tables.py +++ /dev/null @@ -1,173 +0,0 @@ -"""Make test tables. Couple of approaches. GPT.""" - -from datetime import datetime, timedelta -import random -from random import randint, uniform, sample - -import pandas as pd -from faker import Faker - -# Simulate a list of words for column name generation -words = [ - "transaction", "identifier", "processing", "timestamp", "user", "account", "description", - "amount", "balance", "location", "currency", "status", "failure", "note", "reference", - "operation", "duration", "estimate", "category", "filename", "extension", "type", "project", - "client", "supplier", "remark", "address", "email", "comment", "entry", "premium", - "loss ratio", 'expense ratio', "combined ratio", 'loss date' -] - -fake = Faker() - - -def make_column_name(): - # choices with replacement -> sample - return " ".join(random.sample(words, k=random.randint(1, 5))) - - -def make_text_blob(): - return " ".join(sample(words, randint(10, 25))) - - -def make_test_dataframe(n_rows, n_cols): - col_types = random.choices(["int", "float", "str", "date"], k=n_cols) - data = {} - for _ in range(n_cols): - dtype = col_types.pop(0) - col_name = make_column_name() + f' ({dtype})' - if dtype == "int": - data[col_name] = [random.randint(0, 10000) if random.random() > 0.1 else None for _ in range(n_rows)] - elif dtype == "float": - data[col_name] = [round(random.uniform(0, 1e4), 3) if random.random() > 0.1 else None for _ in range(n_rows)] - elif dtype == "str": - data[col_name] = [fake.sentence(nb_words=random.randint(2, 8)) if random.random() > 0.1 else None for _ in range(n_rows)] - elif dtype == "date": - start = datetime(2015, 1, 1) - data[col_name] = [ - (start + timedelta(days=random.randint(0, 4000))).date().isoformat() - if random.random() > 0.1 else None for _ in range(n_rows) - ] - return pd.DataFrame(data) - - -def make_dataframe_set(n): - """Sample dataframes with n rows.""" - def rand_date(): - start = datetime(2000, 1, 1) - return [(start + timedelta(days=randint(0, 10000))).strftime("%Y-%m-%d") for _ in range(n)] - - def rand_float(): - return [f"{uniform(0, 10000):.3f}" for _ in range(n)] - - def rand_int(): - return [str(randint(0, 5000)) for _ in range(n)] - - def rand_text(): - return [make_text_blob() for _ in range(n)] - - def rand_filename(): - return [f"{'_'.join(sample(words, randint(2, 5)))}.pdf" for _ in range(n)] - - def col(colfunc, allow_missing=False): - vals = colfunc() - if allow_missing: - for i in range(randint(1, 3)): - vals[randint(0, len(vals) - 1)] = '' - return vals - - dfs = {} - dfs["floats dates filenames"] = pd.DataFrame({ - make_column_name(): col(rand_float), - make_column_name(): col(rand_date), - make_column_name(): col(rand_filename), - make_column_name(): col(rand_int), - make_column_name(): col(rand_float, allow_missing=True), - }) - - dfs["dense text and numbers"] = pd.DataFrame({ - make_column_name(): col(rand_text), - make_column_name(): col(rand_float), - make_column_name(): col(rand_int), - make_column_name(): col(rand_text), - make_column_name(): col(rand_date), - make_column_name(): col(rand_float, allow_missing=True), - }) - - dfs["mixed data with missing"] = pd.DataFrame({ - make_column_name(): col(rand_float, allow_missing=True), - make_column_name(): col(rand_text, allow_missing=True), - make_column_name(): col(rand_int, allow_missing=True), - make_column_name(): col(rand_date, allow_missing=True), - make_column_name(): col(rand_filename, allow_missing=True), - }) - - dfs["long header names"] = pd.DataFrame({ - "Detailed Instrumentation Configuration Summary": col(rand_text), - "Archive Metadata Extraction Date Field": col(rand_date), - "Overview Record Approximation Notes": col(rand_text), - "Velocity Gradient Approximation Float": col(rand_float), - "Pressure Summary Int Field": col(rand_int), - }) - - dfs["file-centric record"] = pd.DataFrame({ - make_column_name(): col(rand_filename), - make_column_name(): col(rand_date), - make_column_name(): col(rand_text), - make_column_name(): col(rand_float), - make_column_name(): col(rand_int), - make_column_name(): col(rand_date), - make_column_name(): col(rand_filename, allow_missing=True), - }) - - return dfs - - -def make_manual_tests(): - """Five handwritten test tables.""" - df1 = pd.DataFrame({ - "Consideration of Consequences": ["A rather long text value that could wrap badly.", "Short", "A second problematic entry with spaces."], - "Probability": ["Likely", "Unlikely", "Moderate"], - "Expected Value": ["High", "Low", "Moderate"] - }) - - df2 = pd.DataFrame({ - "event_date": ["2024-12-28", "2025-01-05", "2031-06-21"], - "timestamp": ["2024-12-28T14:23:00", "2025-01-05T09:12:45", "2031-06-21T23:59:59"], - "transaction_code": ["ABC-1001-ZZ", "XYZ-2048-AA", "LONG-CODE-2025-EXTREME"] - }) - - df3 = pd.DataFrame({ - "notes": [ - "Item 1: delivered; ready for invoice.", - "Warning -- unit may be faulty?", - "Check: power supply (see page 42)" - ], - "status": ["✓", "✗", "↺"], - "path": [ - "/usr/local/bin/run.sh", - "C:\\Program Files\\App\\main.exe", - "~/Documents/projects/final-report.pdf" - ] - }) - - df4 = pd.DataFrame({ - "Serial": ["A123B456", "X987Y654", "Z000Z111"], - "MD5 Hash": [ - "a5c3e1d7f2b9c3d6f1e4a9b3c7d1e2f3", - "9f1c4d3e7a6b2d5c8e3f9a1b7c6d4e5f", - "ffb1a2c3d4e5f67890123456789abcdef" - ], - "Unwrapped": ["SingleLineValue", "AnotherOne", "NoBreaksHere"] - }) - - arrays = [ - ["Simulation", "Simulation", "Input", "Input", "Output"], - ["ID", "Date Generated", "Model Name", "Parameters", "Result Summary"] - ] - columns = pd.MultiIndex.from_arrays(arrays) - df5 = pd.DataFrame([ - [1, "2024-11-15", "RiskModelV2", "α=0.95, β=3.2", "Stable. 5 iterations. RMSE=0.003"], - [2, "2025-02-04", "SuperModel", "α=0.99, β=2.1", "Converged quickly. RMSE=0.001"], - [3, "2026-08-12", "LongModelNameWithDetails", "α=0.90, β=4.0, γ=1.0", "Diverged on step 4. RMSE=N/A"] - ], columns=columns) - - return [df1, df2, df3, df4, df5] diff --git a/tests/utilities.py b/tests/utilities.py deleted file mode 100644 index 6c7a88c..0000000 --- a/tests/utilities.py +++ /dev/null @@ -1,348 +0,0 @@ -import datetime as dt -from datetime import datetime, timedelta -import logging -import numpy as np -import pandas as pd -from pathlib import Path -import random -import sys -from IPython.display import HTML, display - -from . greater_tables import GT - -# GPT recommended approach -logger = logging.getLogger(__name__) -# Disable log propagation to prevent duplicates -logger.propagate = False -if logger.hasHandlers(): - # Clear existing handlers - logger.handlers.clear() -# SET DEGBUUGER LEVEL -LEVEL = logging.WARNING # DEBUG or INFO, WARNING, ERROR, CRITICAL -logger.setLevel(LEVEL) -handler = logging.StreamHandler(sys.stderr) -handler.setLevel(LEVEL) -formatter = logging.Formatter('%(asctime)s | %(levelname)s | %(funcName)-15s | %(message)s') -handler.setFormatter(formatter) -logger.addHandler(handler) -logger.info(f'Logger Setup; {__name__} module recompiled.') - - -def write_all_tables(out_path='\\s\\telos\\pmir_studynote\\quarto_scratch\\tables.qmd'): - """Write a tester for all tables to a qmd file.""" - header = '''--- -title: {title} -format: - html: - html-table-processing: none - pdf: - include-in-header: prefobnicate.tex ---- - -# Set up code - -```{{python}} -#| echo: true -#| label: setup -%run prefobnicate.py -import proformas as pf - -import greater_tables as gter -import greater_tables.utilities as gtu -gter.logger.setLevel(gter.logging.WARNING) -from IPython.display import display - -``` - -...code build completed. - -# Greater_tables Output - -```{{python}} -#| echo: true -#| label: greater-tables-test -test_gen = gtu.TestDFGenerator() -ans = test_gen.test_suite() -``` - -''' - template = ''' - -## Test Table {k} - -```{{python}} -#| echo: fold -#| label: tbl-greater-tables-test-{i} -#| tbl-cap: Output for test table {k} -hrw = {hrw} -f = gter.GT(ans['{k}'], "{title}", ratio_cols='z', aligners={{'w': 'l'}}, - hrule_widths=hrw) -h = f._repr_html_() -print(f.df.dtypes) -h -``` - -Comments go here. - -''' - tdf = TestDFGenerator() - ans = tdf.test_suite() - out = [header.format(title='All Tables Test - New TestDFGenerator test_suite')] - for i, (k, v) in enumerate(ans.items()): - if v.index.nlevels > 1: - hrw = (1.5, 1.0, 0.5) - else: - hrw = (0,0,0) - out.append(template.format(i=i, k=k, hrw=hrw, title=k.title())) - - p = Path(out_path) - p.write_text('\n'.join(out), encoding='utf-8') - - -# ================================================== -# SUPER DOOPER test df generator with help from GPT -class TestDFGenerator: - """Make excellent test DataFrames.""" - # Load a list of words - _word_list_path = 'C:\\s\\Websites\\new_mynl\\word_lists\\match 12.md' - _word_list_url = 'https://www.mynl.com/static/words.csv' - _word_list = None - - def __init__(self, nan_proportion=0.05, missing_proportion=0, - title=False, sep='_', file_path='local'): - """Initialise the generator.""" - self.nan_proportion = nan_proportion - self.missing_proportion = missing_proportion - self.title = title # whether to apply title to col names - self.sep = sep # separator for column names - if TestDFGenerator._word_list is None: - TestDFGenerator._word_list = TestDFGenerator.load_words(file_path) - # control datatypes - self.data_types = ["int", "float", "str", "year", "date", 'datetime'] - # types: - self.index_probs = np.array([20, 1, 20, 45, 12, 5], dtype=float) - self.index_probs /= self.index_probs.sum() - # control datatypes, types as above - self.data_type_probs = np.array([1, 2, 0.5, 0.5, 0.5, 0.5], dtype=float) - self.data_type_probs /= self.data_type_probs.sum() - - def __repr__(self): - """Return a string representation.""" - return f"TestDFGenerator({len(self.words):,d} words)" - - @staticmethod - def load_words(file_path=''): - """Load a list of words from a file.""" - if file_path == 'local': - file_path = TestDFGenerator._word_list_path - if file_path != '': - p = Path(file_path) - txt = p.read_text(encoding='utf-8') - wl = txt.split('\n') - else: - wl = pd.read_csv(TestDFGenerator._word_list_url, header=None)[0].values - logger.info(f"Loaded wordlist.") # Debug print - return wl - - @property - def words(self): - """Return the word list.""" - random.shuffle(self._word_list) - return self._word_list - - def make_column_names(self, n, g): - """Make n column names each g words long.""" - if self.title: - return [self.sep.join(x).title() for x in zip(*[iter(self.words[:n * g])] * g)] - else: - return [self.sep.join(x) for x in zip(*[iter(self.words[:n * g])] * g)] - - def make_index_data(self, dtype, size): - """Generate index values with natural nesting.""" - if dtype == "int": - values = np.random.randint(0, 100000, size=size) - elif dtype == "float": - values = np.random.uniform(-1e6, 1e6, size=size).round(2) - elif dtype == "str": - values = np.random.choice(self.words, size=size) - elif dtype == 'year': - values = np.random.choice(np.arange(1990, 2030, dtype=int), size=size, replace=False) - elif dtype == "date": - start_date = datetime(2020, 1, 1) - values = [start_date + timedelta(days=random.randint(-5000, 5000)) for _ in range(size)] - elif dtype == "datetime": - start_date = datetime(2020, 1, 1) - values = [start_date + timedelta(days=random.randint(-5000, 5000), - hours=random.randint(0, 23), - minutes=random.randint(0, 59), - seconds=random.randint(0, 59), - microseconds=random.randint(0, 999999)) - for _ in range(size)] - return values # noqa - - def make_multi_index(self, dtypes, levels, size): - """Generate a MultiIndex with natural nesting.""" - # lowest level of index - detailed_index = self.make_index_data(dtypes[-1], size) - # now make the higher levels, here we want far fewer unique values to make repeats - higher_levels = [] - for i in range(levels - 1): - # at level i have i + 2 types?? no just go with 3 - sample = self.make_index_data(dtypes[i], 2 if i==0 else 3) - higher_levels.append(np.random.choice(sample, size=size)) - index_names = np.random.choice(self.words, levels, replace=False) - return pd.MultiIndex.from_arrays([*higher_levels, detailed_index], names=index_names) - - def make_column_data(self, dtype, size): - """Generate column data based on type.""" - if dtype == "int": - picker = np.random.rand() - if picker < 0.5: - return np.random.randint(-10000, 10000, size=size) - else: - return np.random.randint(0, 10**9, size=size) - elif dtype == "float": - picker = np.random.rand() - if picker < 0.4: - return 10. ** np.random.uniform(-9, 1, size=size) - elif picker < 0.8: - return 10. ** np.random.uniform(-1, 10, size=size) - else: - signs = np.random.choice([-1, 1], size=size) - return np.pi ** np.random.uniform(-75, 75, size=size) * signs - elif dtype == "str": - return np.random.choice(self.words, size=size) - elif dtype == 'year': - return np.random.choice(range(1990, 2030), size=size) - elif dtype == "date": - start_date = datetime(2020, 1, 1) - dates = [start_date + timedelta(days=random.randint(-5000, 5000)) for _ in range(size)] - return pd.to_datetime(np.random.choice([d.strftime("%Y-%m-%d") for d in dates], size=size)) - elif dtype == "datetime": - start_date = datetime(2020, 1, 1) - dates = [start_date + timedelta(days=random.randint(-5000, 5000), - hours=random.randint(0, 23), - minutes=random.randint(0, 59), - seconds=random.randint(0, 59), - microseconds=random.randint(0, 999999)) - for _ in range(size)] - return pd.to_datetime(np.random.choice([d.strftime("%Y-%m-%d %H:%M:%S.%f") for d in dates], size=size)) - - def make_test_dataframe(self, - num_rows=10, - num_columns=5, - num_index_levels=1, - num_column_levels=1, - column_name_length=3, - dtype_label=True, - index_types=None, - title=False, - sep='_' - ): - """ - Generate a random pandas DataFrame with diverse structures for testing. - - Parameters: - - num_rows (int): Number of rows. - - num_columns (int): Number of columns. - - num_index_levels (int): Levels in the index (1+). - - num_column_levels (int): Levels in the columns (1+). - - column_name_length (int): Words per column name. - - dtype_label (bool): Whether to tag columns with their type. - - index_types (list): List of index data types for each level. - - words (list): List of words for generating column names. - - Returns: - - pd.DataFrame: A test DataFrame with diverse structures. - """ - # update - self.title = title - self.sep = sep - # Generate column names - col_names = self.make_column_names(num_columns, - max(1, column_name_length - (1 if dtype_label else 0))) - - # Randomly select index data types for each level - if index_types is None: - index_types = np.random.choice(self.data_types, num_index_levels, p=self.index_probs, replace=True) - if not isinstance(index_types, (tuple, list)): - index_types = [index_types] - if len(index_types) < num_index_levels: - # well... - index_types = (index_types * 10)[:num_index_levels] - - # Generate hierarchical MultiIndex with natural grouping - if num_index_levels > 1: - index = self.make_multi_index(index_types, num_index_levels, num_rows) - else: - name = np.random.choice(self.words, 1)[0] - index = pd.Index(self.make_index_data(index_types[0], num_rows), name=name) - - # Data types - dtype_choices = np.random.choice(self.data_types, num_columns, p=self.data_type_probs, replace=True) - - # Generate column structure - if num_column_levels > 1: - columns = self.make_multi_index(['str'] * num_column_levels, num_column_levels, num_columns) - # don't want the index names - columns.names = [''] * num_column_levels - else: - columns = pd.Index([f"{col} {dtype}" if dtype_label else col - for col, dtype in zip(col_names, dtype_choices)], - name="Column") - - # Generate data - data = {col: self.make_column_data(dtype, num_rows) for col, dtype in zip(columns, dtype_choices)} - df = pd.DataFrame(data, index=index, columns=columns) - - # Convert date columns to datetime dtype - for col, dtype in zip(columns, dtype_choices): - if dtype == "date": - df[col] = pd.to_datetime(df[col], errors="coerce") - - # Introduce NaNs - num_nans = int(self.nan_proportion * num_rows * num_columns) - for _ in range(num_nans): - df.iat[random.randint(0, num_rows - 1), random.randint(0, num_columns - 1)] = np.nan - - # Introduce radical None values - if self.missing_proportion: - num_missing = int(self.missing_proportion * num_rows * num_columns) - for _ in range(num_missing): - df.iat[random.randint(0, num_rows - 1), random.randint(0, num_columns - 1)] = None - - df = df.sort_index().sort_index(axis=1) - return df - - __call__ = make_test_dataframe - - def test_suite(self): - """Make a dict of test dataframes with different characteristics.""" - ans = {} - - ans['basic'] = self.make_test_dataframe(num_rows=10, num_columns=8, - num_index_levels=1, num_column_levels=1, - column_name_length=1, - index_types=['int']) - - ans['timeseries'] = self.make_test_dataframe(num_rows=20, num_columns=3, - num_index_levels=1, num_column_levels=1, - column_name_length=4, title=True, sep=' ', - index_types=['datetime']) - - ans['multiindex'] = self.make_test_dataframe(num_rows=10, num_columns=5, - num_index_levels=3, num_column_levels=1, - column_name_length=4, title=True, sep=' ', - index_types=['int', 'str']) - - ans['multicolumns'] = self.make_test_dataframe(num_rows=10, num_columns=5, - num_index_levels=1, num_column_levels=3, - column_name_length=4, title=True, sep=' ', - index_types=['int', 'str']) - - ans['complex'] = self.make_test_dataframe(num_rows=20, num_columns=10, - num_index_levels=3, num_column_levels=3, - column_name_length=4, - index_types=['int', 'str']) - - return ans