Actuarial notation with L^aT_eX

Presentation

Actuaries denote various quantities of life contingencies like present values of life insurances and life annuities, annual premiums, or reserves using a whole array of symbols. The highly descriptive, yet compact, notation is subject of an international standard since 1898.

Actuarial notation is characterized by auxiliary symbols positioned in subscript and superscript on both sides of a principal symbol, something notoriously difficult to achieve consistently in LaTeX. It also requires some unusual symbols not found in standard mathematics packages, like the angle denoting a duration in insurance and annuity symbols.

actuarialsymbol and actuarialangle are two actively maintained LaTeX packages providing facilities to compose actuarial symbols of life contingencies and financial mathematics.

Obtaining the packages

actuarialsymbol and actuarialangle are distributed through the Comprehensive TeX Archive Network (CTAN). They are also part of TeX Live and MiKTeX.

• actuarialsymbol on CTAN
• actuarialangle on CTAN

The source code of both packages is hosted on GitLab. You may file bug reports, comments or feature requests there.

• actuarialsymbol on GitLab
• actuarialangle on GitLab

Both packages are licensed under the LaTeX Project Public License.

Authors

David Beauchemin (davebulaval) and Vincent Goulet (vigou3), École d’actuariat, Université Laval.

Features

actuarialangle

• Typesetting of a nice looking angle symbol with command \angl (and shortcuts \angln, \anglk and \anglr for common cases).
• Package option to insert a thin or thick space between the symbol under the angle and the right descender.
• Typesetting of an over angle bracket used to emphasize joint status in life contingencies symbols with command \overanglebracket. The rule thickness and spacing relative to the statuses underneath the bracket match those of the angle symbol.

actuarialsymbol

• Composition of an arbitrary actuarial symbol with the generic command \actsymb. The command has mandatory arguments for the principal symbol and for the auxiliary symbol in the lower right corner. Auxiliary symbols in the lower left, upper left and upper right corners are optional. Subscripts and superscripts are vertically aligned and positioned following TeX’s defaults.

• Shortcuts to easily and consistently compose most common actuarial symbols of life contingencies. The nomenclature clearly identifies the symbol being typeset (e.g. \Ax, \ax, \sx) and makes clever use of the star (e.g. \Ax* for \bar{A} and \ax** for \ddot{a}). See below for a sneak peek and the package documentation for the complete list of shortcuts.

• Extended syntax of \actsymb and shortcuts to typeset symbols for premiums, reserves and paid-up insurance.

• Facilities to define new shortcuts that automatically gain * and ** variants.

• Typesetting of two-letter actuarial symbols with command \twoletsymb and a number of shortcuts for the most common combinations like (IA) and (DA).

• Positioning of precedence numbers (or decrement order) above or below statuses of multiple lives contracts with the generic commands \nthtop and \nthbottom. Shortcuts for first, second and third precedence order are available and options to control positioning of the numbers relative to the corresponding status.

• Appendix A of the package documentation lists the commands to typeset a large selection of life contingencies symbols with actuarialsymbol and actuarialangle loaded.

Sneak peek

The excerpt from the package documentation below lists the shortcut for life table, insurance and annuity symbols.

Alternatives

Authors often use ad hoc constructions like {}_tA_x to put subscripts and superscripts in front of a symbol. This notation quickly becomes a nightmare to parse mentally and the source code has little relationship to the actual significance of the symbol. That said, the worst practical drawback to this approach is probably that there is no way to ensure that subscripts and superscripts on either side of the principal symbol are aligned vertically. Try something like {}_tA_x^{(m)}, for example.

The package mathtools provides a command \prescript to put a subscript or superscript to the left of an argument. This works well when the argument (or principal symbol) has sub- and superscripts on all four corners, but otherwise the auxiliary symbols may end up at different heights.

Finally, various packages tailored for specific disciplines offer the possibility to position sub and superscripts on the left, for example tensor for tensors or mhchem for isotopes.