Actuarial computation deals with quantifying and redistributing risk in insurance and finance. Risks refer to financial losses and may relate to health, cars, life, and financial investments, etc. Risks are redistributed by grouping many individuals and analyzing the whole group to determine premiums and risk probabilities, etc.  The Wolfram Language provides extensive support for models, data, and computation related to finance, probability, and statistics. In life insurance, important aspects include time value of money with either deterministic or stochastic models of lifetimes. In non-life insurance, important parts include the frequency and size of claims for a group, either short term or long term.

Basic Concepts »

Probability — loss probability

Expectation — expected value of claims or premiums

NormalDistribution  ▪  RandomVariate  ▪  EstimatedDistribution

Life Insurance (Deterministic) »

Cashflow — cash flow of premiums

Annuity — regular premium or pension payments

TimeValue — time value of a death benefit

Life Insurance (Stochastic) »

SurvivalModelFit — nonparametric estimation of lifetime distributions

GompertzMakehamDistribution — common parametric lifetime distribution

BenktanderGibratDistribution  ▪  BenktanderWeibullDistribution

Non-Life Insurance (Collective Risk) »

PoissonDistribution — claim frequency distribution

ExponentialDistribution — claim severity distribution

CompoundPoissonDistribution — claim distribution in collective risk model

SplicedDistribution — splicing body and tail claim distribution

ParetoDistribution  ▪  WeibullDistribution  ▪  LogNormalDistribution

Non-Life Insurance (Surplus & Ruin) »

CompoundPoissonProcess — long-term claims process

CompoundRenewalProcess — general long-term claims process

RandomFunction  ▪  EstimatedProcess  ▪  TransformedProcess

Actuarial Data

MortalityData — life tables etc. for many countries and dates