Mixed Dividend Strategy To Explore In The Risk Model

In the classical compound Poisson risk model, the claim amounts and the interclaim times are always assumed to be independent. In fact, this hypothes is inadequate to de-pict the realistic circumstances, so more and more risk models with interclaim-dependent claim sizes have been studied. Risk models under dividend strategies have been the sub-ject of several research papers since it has been initially proposed by De Finetti(1957) for a binomial model. In this thesis we consider the classical risk model with hybrid dividend strategy and find some results, then we generalize the risk model to a model with de-pendence structure between the claim amounts and the inter-claim times. We obtain the integro-differential equation satisfied by the expected discounted penalty function with the corresponding boundary conditions.This paper is divided into two chapters according to contents:Chapter 1 gives several results for the classical compound Poisson risk model. Firstly, we review the two important dividend strategies in risk theory and introduce the specific risk model which studied in the context. Then we obtain some results, for example, the integro-differential equations satisfied by the Gerber-Shiu expected discounted penalty function and the expected discounted dividends function and special result when the claim amounts are exponentially distributed.In Chapter 2, we study some questions with interclaim-dependent claim sizes. Firstly we introduce the preliminary knowledge with classical FGM copula dependence between interclaim arrivals and claim sizes. Then we find the integro-differential equation satisfied by the Gerber-Shiu expected discounted penalty function and the corresponding bound-ary conditions.