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.
Highlights
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 mutually independent
We consider a jump-diffusion risk process compounded by a geometric Brownian motion, and assume that the claim sizes and claim intervals are dependent
Various papers in ruin theory modify the classical Poisson risk model to describe the surplus process of an insurance portfolio
Summary
Various papers in ruin theory modify the classical Poisson risk model to describe the surplus process of an insurance portfolio. I=1 where u ≥ 0 is the initial surplus, c > 0 is the positive constant premium income rate, S (t ) = ∑ Xi is the aggregate claims process, in which i=1. { }T ∞ i i=1 is a sequence of positive random variables. { }T ∞ i i=1 and the claim sizes {Xi , i ≥ 1} are mutually independent. Various results have been obtained concerning the asymptotic behavior of the probability of ruin for dependent claims, see [8]-[14], as well as the references therein. Motivated by the results of Zhao [14], the main aim of this paper is to modify the risk model (Equation (1)), and establish integro-differential equations for the Gerber-Shiu function and the ultimate ruin probability in the new risk model
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