Study On Some Problems Of Markov-modulated Dual Risk Models

In risk theory,dividend problems have become a hot issue recently.The risk models under dividend strategy are also received widespread attention.With the development of social economy and people thinking more many-sided,many researchers are interest in the dual risk model.In the classic dual risk model,we does not consider external factors,however,the external economic environment in real life changes constantly.So in this paper,we mainly study some related bankruptcy and dividend problems in the Markov-modulated dual model under a barrier strategy or a threshold dividend strategy.According to these research details,this paper is divided into four chapters:In Chapter 1,we simply introduce the research status and development as well as the structural arrangement in this paper.In Chapter 2,we consider the Markov-modulated dual risk model with proportional attract investment under a threshold dividend strategy.We derive the integro-differential equations satisfied by the moment-generating function,the 9)th moment of the discounted dividend payments and the expected total discounted dividends payments until ruin.A numerical sinc method is proposed.In Chapter 3,we consider the Markov-modulated dual risk model with diffusion and randomized observation time under a barrier strategy.We derive the integro-differential equations satisfied by the expected total discounted dividend payments until ruin,the Laplace transform of ruin time and the ruin probability.In the two-state dual risk model,explicit expressions for the expected total discounted dividends payments until ruin and the Laplace transform of ruin time are obtained when the gains are exponentially distributed.Moreover,some numerical illustrations are presented.In the last chapter,we sum up what we have done in this paper.