The module extends the mathematical framework developed in MATH3063 in order to enable modelling of long term financial transactions where the various cash flows are contingent on the death or survival of several lives, or where there are several competing sources of decrement present. Having extended this framework, we can address pricing and reserving issues for contracts on a pair of lives, such as a husband and wife.
The module begins by extending the notion of a life table to several lives, as a precursor to examining assurances on a pair of lives where the benefit is paid on the first (joint life assurance) or last (last survivor assurance) of the pair to die. Assurances payable only on a specified ordering of the deaths (contingent assurances) are also covered, as are correspondingly ordered annuities (reversionary annuities).
Attention then turns to a single life subject to several competing sources of decrement who may leave the population of active members by age retirement, by ill-health retirement, by death, or by leaving employment covered by the scheme. Both multiple-state and multiple-decrement models are employed in such contexts, and both are examined.
The concepts of aggregate claim and cash-flow process are explained. Then Poisson process are used to model the number of claims, and the distribution of inter-arrival claims are discussed. The concept of ruin probability is covered where compound poison processes and simulation techniques are covered to calculate various type of finite and infinite horizon ruin probabilities. Next, the method of chain ladder and their application in delay trainable are studied where inflation is allowed and statistical models are applied. Finally, Bornhuetter-Ferguson method for estimating outstanding claim amounts are investigated.