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 JAMP  Vol.4 No.11 , November 2016
Integro-Differential Equations for a Jump-Diffusion Risk Process with Dependence between Claim Sizes and Claim Intervals
Abstract: 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.
Cite this paper: Gao, H. (2016) Integro-Differential Equations for a Jump-Diffusion Risk Process with Dependence between Claim Sizes and Claim Intervals. Journal of Applied Mathematics and Physics, 4, 2061-2068. doi: 10.4236/jamp.2016.411205.
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