Actuarial Modelling: Understanding Actuarial Models, Claim-frequency distribution, Claim-severity distribution, Aggregate-loss models, Risk measures Principles of Actuarial models, Actuarial Models for Sickness Insurance, Life Insurance Models, Actuarial Models for Disability Annuities, Pensions Plans Loss distributions in insurance, parameterized families of loss distributions and estimation of the parameters. Re-insurance strategies, excess of loss (stop-loss) re-insurance, proportional re-insurance.
Risk models of short term general insurance: the individual risk model.
Properties of the aggregate claim process. Stieltjes integrals and their application in individual risk models.
Risk models of short term general insurance: the collective risk model. Modelling the claim number process, the aggregate claim process. Properties of the aggregate claim process. The compound Poisson model, the compound Binomial model, the compound Negative Binomial model.
Risk models of short term general insurance: re-insurance in risk models. Excess of loss and proportional re-insurance. Parameter uncertainty (accident proneness).
Risk models of short term general insurance: Panjer's recursive algorithm and similar algorithms.
Valuation, under fixed interest rates, of state dependent and transition dependent benefits, state dependent premiums, in a multi-state Markov model. The equivalence principle and the equation of value of an insurance policy. Examples from life insurance, disability insurance and pensions. Policy values and reserves. Recursive calculation of reserves.
Run-off triangles: chain ladder method.