actuarialmath

actuarialmath - Solve Life Contingent Risks with Python

This Python package implements fundamental methods for modeling life contingent risks, and closely follows the coverage of traditional topics in actuarial exams and standard texts such as the "Fundamentals of Actuarial Math - Long-term" exam syllabus by the Society of Actuaries, and "Actuarial Mathematics for Life Contingent Risks" by Dickson, Hardy and Waters.

Overview

The package comprises three sets of classes, which:

1. Implement general actuarial methods

   • Basic interest theory and probability laws

   • Survival functions, expected future lifetimes and fractional ages

   • Insurance, annuity, premiums, policy values, and reserves calculations

2. Adjust results for

   • Extra mortality risks

   • 1/mthly payment frequency using UDD or Woolhouse approaches

3. Specify and load a particular form of assumptions

   • Recursion inputs

   • Life table, select life table, or standard ultimate life table

   • Mortality laws, such as constant force of maturity, beta and uniform distributions, or Makeham's and Gompertz's laws

Quick Start

1. pip install actuarialmath

   • also requires numpy, scipy, matplotlib and pandas.

2. Start Python (version >= 3.10) or Jupyter-notebook

   • Select a suitable subclass to initialize with your actuarial assumptions, such as MortalityLaws (or a special law like ConstantForce), LifeTable, SULT, SelectLife or Recursion.

   • Call appropriate methods to compute intermediate or final results, or to solve parameter values implicitly.

   • Adjust the answers with ExtraRisk or Mthly (or its UDD or Woolhouse) classes.

Examples

::

SOA FAM-L sample question 5.7

from actuarialmath import Recursion, Woolhouse

initialize Recursion class with actuarial inputs

life = Recursion().set_interest(i=0.04)
.set_A(0.188, x=35)
.set_A(0.498, x=65)
.set_p(0.883, x=35, t=30)

modfy the standard results with Woolhouse mthly approximation

mthly = Woolhouse(m=2, life=life, three_term=False)

compute the desired temporary annuity value

print(1000 * mthly.temporary_annuity(35, t=30)) # solution = 17376.7

::

SOA FAM-L sample question 7.20

from actuarialmath import SULT, Contract life = SULT()

compute the required FPT policy value

S = life.FPT_policy_value(35, t=1, b=1000) # is always 0 in year 1!

input the given policy contract terms

contract = Contract(benefit=1000, initial_premium=.3, initial_policy=300, renewal_premium=.04, renewal_policy=30)

compute gross premium using the equivalence principle

G = life.gross_premium(A=life.whole_life_insurance(35), **contract.premium_terms)

compute the required policy value

R = life.gross_policy_value(35, t=1, contract=contract.set_contract(premium=G)) print(R-S) # solution = -277.19

Resources

1. Jupyter notebook <https://terence-lim.github.io/notes/faml.ipynb>_ or run in Colab <https://colab.research.google.com/github/terence-lim/terence-lim.github.io/blob/master/notes/faml.ipynb>_, to solve all sample SOA FAM-L exam questions

2. User Guide <https://actuarialmath-guide.readthedocs.io/en/latest/>, or download pdf <https://terence-lim.github.io/notes/actuarialmath-guide.pdf>

3. API reference <https://actuarialmath.readthedocs.io/en/latest/>_

4. Github repo <https://github.com/terence-lim/actuarialmath.git>_ and issues <https://github.com/terence-lim/actuarialmath/issues>_