نسترن زنگنه پور

Insurance mathematics is application of probability theory to modeling insurance risk. The collective risk theory based on the stochastic processes that correct description of the claims that appear in the frame of any insurance policy. Through the stochastic processes can construct models for the random fluctuations of the financial reserves, that are helpful for the coverage of the claims. In this thesis about applications of self-exciting Hawkes processes in insurance mathematics.The insurer’s risk model with claim arrivals based on general compound Hawkes processes and show that it is suitable to model empirical insurance data. This risk model for certain classes of insurance claims includes clustering of claim payments.The theoretical properties law of large numbers and functional central limit theorem are investigated for this model and derive a pure diffusion approximation which allows analytical calculation of ruin probabilities. This approximation to study the influence of replacing the classical Poisson arrival process by a general compound Hawkes process and risk enhancing on optimal investment strategies for an insurer in an incomplete market by applying results from asset–liability management. The objective is to maximize the insurer’s expected terminal wealth while minimizing the variance of the terminal wealth. The optimal strategy and the mean–variance efficient frontier in closed forms is obtained by using the stochastic linear-quadratic (LQ) control technique.