A Class Of Optimal Dividends Problem With Disturbance Of The Classical Model

This paper considered the optimal dividend payment for the compound Pois-son model disturbed by diffusion under consideration of the time value of ruin. The optimal dividend problem has become a research focus in actuarial mathe-matics since the dividend problem of the classical risk model was put forward, and lots of references have generalized it so as to satisfy the requirements of reality. In this paper, we introduce a value function which considers both expected divi-dends and the time value of ruin. We study the optimal dividend problem in the compound Poisson model disturbed by diffusion under the new value function.This dissertation is divided into four chapters.In the first chapter, we introduce the importance and the international re-search progress of the optimal dividend problem.In the second chapter, we list some preliminaries such as the compound Poisson model disturbed by diffusion, the value function and so on.In the third chapter, we show that, in case the admissible dividend payment intensity is bounded, the threshold strategy is optimal strategy for exponential distributed claim sizes.In the forth chapter, we show that the barrier strategy is the optimal dividend payment in the case that the admissible dividend payment intensity is unbounded and exponential distributed claim sizes.