actuarialmath 0.0.7

A package for life contingent risks

This package implements fundamental methods for modeling life contingent risks, and closely follows traditional topics covered 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 concepts

   1. Basic interest theory and probability laws

   2. Survival functions, future lifetimes and fractional ages

   3. Insurance, annuity, premiums, policy values, and reserves calculations

2. Adjust results for

   1. Extra risks

   2. 1/mthly payments using UDD or Woolhouse approaches

3. Specify and load a particular form of assumptions

   1. Life table, select life table, or standard ultimate life table

   2. Mortality laws, such as constant force of maturity, beta and uniform distributions, or Makeham’s and Gompertz’s laws

   3. Recursion inputs

Quick Start

1. pip install actuarialmath

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

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

4. If needed, adjust the answers with ExtraRisk or Mthly (or its UDD or Woolhouse) classes.

Examples

# SOA FAM-L sample question 5.7
from actuarialmath.recursion import Recursion
from actuarialmath.woolhouse import 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.sult import SULT   # use Standard Ultimate Life Table
from actuarialmath.policyvalues import 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. Colab or Jupyter notebook, to solve all sample SOA FAM-L exam questions

2. Online tutorial, or download pdf

3. Code documentation

4. Github repo and issues