Dependent Risk Model. A Threshold Dividend

A dependent risk model between claim sizes and interclaim arrivals was proposed by Boudrcault et.al.in reference[3].In this paper we generalize this correlation based on the model,and wc use the threshold dividend strategy with debit.The aim of this thesis is to get the results as follows:one is its integro-differential equations satisfied by the Gerbcr-Shiu expected discounted penalty function,another is its integro-differential equations satisfied by the dicounted dividend function.This paper is dividend into three chapters according to contents:Chapter 1 is mainly to introduce the development process of risk model from the independent model to the dependcnt model,and we introduce two models with debit of the radom variables.Then we describe the results in hand.At last we put up the qucstions we will discuss in the paper.In chapter 2,we get the integro-diffcrential equations satisficd by the Gerbcr-Shiu expected discounted penalty function directly in the first section.In section two,section three and four,we derive the functions by the means of conditioning the first claim time and the claim amount.In section five,we give some special examples to conduct some special integro-differential equations satisfied by the Gerber-Shiu discounted penalty function which arc identical with references[16]and[17],which proves this paper generalizes some correlation risk models.In chapter 3,in the first section we exemplify some basic acknowledge which is helpful when we conduct the equations later,we get the integro-differential equations satisfied by the disconntcd dividend functions directly in section two.In section three we conduct the integro-differential equations satisfied by the discounted dividend functions which are identical with reference[11].