With Constant Value Of The Bonus Limits Of A Class Of Dependent Risk Model

In the classical risk model, the claim amounts and the interclaim times are always assumed to be independent. But in fact, this hypothesis is inadequate to depict the realistic circumstances, so more and more risk models with dependence between interclaim arrivals and claim sizes have been studied. At the same time, dividend is also a hot topic.This paper proposed the compound Poisson risk model with classical FGM copula dependence between interclaim arrivals and claim sizes in the presence of a constant dividend barrier. In this paper, we study the risk model and get an integro-differential equation for Gerber-Shiu expected discounted penalty function in the risk model and get the solution to the equation. Then we analyze the expected discounted dividend function before ruin in the same risk model. An integro-differential equation is derived and then solved.This paper is divided into four chapters according to contents:Chapter 1 is preface. First we review the development and the generalization of the risk model with dependence between interclaim arrivals and claim sizes and the risk model with dividend barrier, list some related probability knowledge and the knowledge of the classical FGM copula function, then we introduced the compoud Poisson risk model with classical FGM copula dependence between interclaim arrivals and claim sizes in the presence of a constant dividend barrier.In Chapter 2, we consider the compound Poisson risk model with classical FGM copula dependence between interclaim arrivals and claim sizes in the presence of a constant dividend barrier, study the Gerber-Shiu expected discounted penalty function under this risk model, and get the integro-differential equation satisfied by the Gerber-Shiu expected discounted penalty function and the boundary conditions: Then we get the expression of the solution to the equation: where m∞,δ(u) is the Gerber-Shiu expected discounted penalty function without the div-idend barrier,ζ1,ζ2 are the coefficients which satisfy some equations, andIn Chapter 3, we continue studying the compound Poisson risk model with classical FGM copula dependence between interclaim arrivals and claim sizes in the presence of a constant dividend barrier, and get the integro-differential equation satisfied by the expected discounted dividend function before ruin and the boundary conditions:Moreover, we get the expression of the solution to the equation:In Chapter 4, we will correct three mistakes in reference [3].