A Class Of Dependent Risk Model Number Of The Results

A dependent risk model between claim sizes and interclaim arrivals was proposed by Boudreault,et al.in 2006.In this paper we generalize this correlation to copulas,and we use the barrier dividend strategy in this paper.The aim of this thesis is to get the results as follows:one is its integro-differential equations satisfied by the Gerber-Shiu discounted penalty function,another is its integro-differential equations satisfied by the dicounted dividend function,finally we get the integro-differential equations satisfied by the moment genarating functions of the dividends and the relation of the moments of dividends. This paper is dividend into four chapters according to contents:Chapter 1 is mainly to introduce the development process of risk model from the independent model to the dependent model,and we introduce the Copula correlation of the radom variables.The we introduce some knowledge of the copula functions.In this paper we mainly use the Sklar theorem to connect the distributions of random variables with their joint distribution.In chapter 2.we get the integro-differential equation satisfied by the Gerber-Shiu discounted penalty function by the means of conditioning the first claim time and the claim amount in the first section.In section two,we use some special Copula functions as examples to conduct some special integro-differential equations satisfied by the Gerber-Shiu discounted penalty function which are identical with references,which proves this paper generalizes some correlation risk models.In chapter 3.we mainly derive the integro-differential equation satisfied by the discounted dividend functions in seetionon.In section two,we use some special Copula functions as examples to conduct some special integro-differential equations satisfied by the discounted dividend functions which are identical with references.In chapter4,we derive the integro-differential equation satisfied by the moment genarating functions of the dividends in section one.In section two we get the relationship of the moments of the dividends by using the relationship of the moment genarationg functions and the moments of divideds.