Relevant Problems Of Dual Risk Models Under Two Kinds Of Dividend

Since 1957, the dividend strategy was ?rst introduced and discussed by De. Finetti in the discrete time risk model. From then on, the dividend problem has become one of the important issues which insurance companies and actuarial science must face. Meanwhile,in recent years, a barrier dividend strategy or a threshold dividend strategy has attracted a lot of attention in the dual risk model. Actually, under a certain conditions the abovementioned dividend strategy has its some limitations, so the hybrid dividend strategy which is a generalization of the barrier dividend strategy and the threshold dividend strategy raises extensive attention of more and more scholars. For the classical risk model,a lot of literatures have given many discussions for the ruin problems when the individual claims have generalized Erlang(n)distributions. Due to the relationship of the classical risk model and the dual risk model, the ?rst dividend problems have been discussed with a barrier dividend strategy in the dual risk model. So this paper is based on the dual risk model, and we study the related dividend problem of a hybrid dividend strategy and the?rst dividend problem of a barrier dividend strategy. According to these research details,this paper is divided into two chapters:In chapter one, we ?rst introduce the current situation of the dividend strategy, the hybrid dividend strategy, and the dual risk model with di?usion and generalized Erlang(n)interclaim times; secondly, we derive the integral di?erential equation of the expected discounted dividend function, and its identical integral equation when n = 1; ?nally,the integral di?erential equation and corresponding boundary conditions of the moments,moment-generating functions are brie?y discussed.In chapter two, the preparatory work of the ?rst dividend problem and the dual risk model without di?usion in the presence of a barrier dividend strategy are brie?y introduced; furthermore, when the initial value is b, the expression of the joint density function of the ?rst dividend time and the aggregate dividends is given when the gains are the mixture of exponential distribution and Erlang(2) distribution. In addition, we also acquire the expression of the joint density function and the density of the ?rst dividend time.