The Gerber–Shiu discounted penalty functions for a risk model with two classes of claims
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摘要
In this paper, we consider the ruin problems for a risk model involving two independent classes of insurance risks. We assume that the claim number processes are independent Poisson and generalized Erlang(n) processes, respectively. When the generalized Lundberg equation has distinct roots with positive real parts, both of the Gerber–Shiu discounted penalty functions with zero initial surplus and the Laplace transforms of the Gerber–Shiu discounted penalty functions are obtained. Finally, some explicit expressions for the Gerber–Shiu discounted penalty functions with positive initial surplus are given when the claim size distributions belong to the rational family.
论文关键词:Gerber–Shiu discounted penalty function,Integro-differential equations,Generalized Lundberg equation,Laplace transform
论文评审过程:Received 30 March 2008, Revised 8 January 2009, Available online 17 January 2009.
论文官网地址:https://doi.org/10.1016/j.cam.2009.01.002