Title: On the expected penalty function for a risk model perturbed by diffusion

Authors: Jie-Hua Xie; Wei Zou

Addresses: Department of Science, NanChang Institute of Technology, NanChang city, JiangXi Province 330099, China. ' Department of Science, NanChang Institute of Technology, NanChang city, JiangXi Province 330099, China

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.

Keywords: continuous time risk modelling; expected penalty function; generalised Erlang(2) process; diffusion process; Laplace transform.

DOI: 10.1504/IJCAT.2012.046044

International Journal of Computer Applications in Technology, 2012 Vol.43 No.2, pp.140 - 146

Available online: 24 Mar 2012 *

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