On the expected penalty function for a risk model perturbed by diffusion
by Jie-Hua Xie; Wei Zou
International Journal of Computer Applications in Technology (IJCAT), Vol. 43, No. 2, 2012

Abstract: In this paper, a continuous time risk model perturbed by an independent diffusion (Wiener) process is considered. The claim number process is assumed to be a generalised Erlang(2) process. Both the expected penalty functions with zero initial surplus and the Laplace transforms of the expected penalty functions are obtained from an integro-differential equations system. The analytic expressions for expected penalty functions are derived when the claim amounts are exponentially distributed. Moreover, the closed form expressions for the ruin probabilities are proposed. Finally, numerical results are also provided to illustrate the applicability of the main result.

Online publication date: Tue, 27-Mar-2012

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