Actuarial Models in General Insurance

Course 3A of the Association's actuarial programme covers the mathematical models on which premium rates, reserves and reinsurance in general insurance are built. From utility theory and aggregate loss models to the choice of distributions, parameter estimation, credibility theory, Bayesian methods, the effect of deductibles and limits, and model validation. Its depth matches international actuarial education syllabuses; every method is worked through in a step-by-step calculation.

Course programme

1. Utility theory and insurance economics — risk aversion, maximum and minimum premium, premium principles.
2. Individual risk model — aggregate loss of a portfolio, safety loading, probability of ruin.
3. Collective risk model — compound Poisson, Panjer recursion, tail approximations.
4. Claim frequency and severity models — the (a, b, 0) class, mixed Poisson, heavy tails.
5. Parameter estimation and model selection — method of moments, maximum likelihood, goodness-of-fit tests, AIC and BIC.
6. Credibility theory — limited fluctuation, the Bühlmann model, application to group rating.
7. Bayesian models and conjugate distributions — Poisson–gamma, beta–binomial, link with credibility.
8. Coverage modifications: deductibles, limits, inflation — payment per loss and payment per payment, the leveraging effect of inflation.
9. Simulation and model validation — Monte Carlo, simulation accuracy, back-testing against history, model governance.

Each lesson comes with notes containing a table of notation, a worked example and practice problems, plus a lesson test. The course final test consists of 30 questions and 10 calculation problems; ASAB certificate.

Duration: 9 video lessons, 2 h 17 min of video + lesson tests and a final test.