Integro-Differential Equations for a Jump-Diffusion Risk Process with Dependence between Claim Sizes and Claim Intervals  

作　　者：Heli Gao Heli Gao(Department of Mathematics, Binzhou University, Binzhou, China)

机构地区：[1]Department of Mathematics, Binzhou University, Binzhou, China

出　　处：《Journal of Applied Mathematics and Physics》2016年第11期2061-2068,共8页应用数学与应用物理（英文）

摘　　要：The classical Poisson risk model in ruin theory assumed that the interarrival times between two successive claims are mutually independent, and the claim sizes and claim intervals are also mutually independent. In this paper, we modify the classical Poisson risk model to describe the surplus process of an insurance portfolio. We consider a jump-diffusion risk process compounded by a geometric Brownian motion, and assume that the claim sizes and claim intervals are dependent. Using the properties of conditional expectation, we establish integro-differential equations for the Gerber-Shiu function and the ultimate ruin probability.The classical Poisson risk model in ruin theory assumed that the interarrival times between two successive claims are mutually independent, and the claim sizes and claim intervals are also mutually independent. In this paper, we modify the classical Poisson risk model to describe the surplus process of an insurance portfolio. We consider a jump-diffusion risk process compounded by a geometric Brownian motion, and assume that the claim sizes and claim intervals are dependent. Using the properties of conditional expectation, we establish integro-differential equations for the Gerber-Shiu function and the ultimate ruin probability.

关 键 词：Jump-Diffusion Risk Process Diffusion Geometric Brownian Motion Gerber-Shiu Function 

分 类 号：O17[理学—数学]