|
1(a) Decision Theory Optimum strategies, loss/risk functions, expected utility principle, rationality principles and the likelihood principle of optimal strategies, Minimax criterion, proper Bayes rules, model selection, the travel insurance example. (b) Applications of Probability Theory to actuarial risk models Brief review of probability theory: moment generating functions and distribution functions for finite sums of independent random variables (obeying the Bernoulli, geometric, negative binomial, binomial, Poisson, Normal, and exponential distribution). (c) The collective risk model (aggregate loss models) The compound risk model for aggregate claims, convolutions for the calculation of the distribution function and the probability function of the compound risk model, the moment generating function and the probability generating function of the aforementioned model, mean and variance calculation of the compound risk model, the compound Poisson risk model, the compoun
d binomial risk model, the compound geometric risk model, sums of independent compound Poisson random variables, the compound risk model from the insurer/reinsurer point of view for simple forms of proportional and stop‐loss reinsurance (subject to a deductible), net stop‐loss premiums, the R (a, b, 0) family of distributions (satisfy Panjer's equation) for the random variable corresponding to the number of claims (frequency distribution), the probability function recursion (Panjer's recursion) of the total aggregate losses [for the class R (a, b, 0). (d) The individual risk model (group insurance models) The aggregate loss models (individual risk model) for insurance contracts (finite sums of independent but not necessarily identically distributed random variables), the mean and the variance under the specific risk model, applications of the aforementioned model to groups of life insurance contracts (with certain probability of death within a year) and to
groups of non‐life insurance contracts, the compound Poisson approximation for the individual risk model. (e) Ruin Theory The general surplus process of an insurance portfolio, the Poisson process and waiting times for the number of the events in a given time interval, the classical compound Poisson surplus process and its moment generating function, the adjustment coefficient and Lundberg's inequality, the integro‐differential equation for the ruin probability psi ( u) , closed form expressions of the ruin probability, psi ( u) , as solution of an ordinary differential equation (which is a consequence of the aforementioned integro‐differential equation for specific claim amount distributions, eg. exponential and mixture of exponentials), definition of the discrete time surplus process and recursive evaluation of the finite ruin probability psi(u,t), the probability of ruin and the adjustment coefficient under a simple reinsurance schemes. (f) Claim
reserving methods Introduction to concept of IBNR claims and outstanding report claims reserve, delay or Run‐off triangles: the basic chain ladder method, inflation‐adjusted chain ladder method, the average cost per claim method, Loss ratios, the Bornjuetter‐Ferguson method for projecting run‐off triangles.
|