About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 401562, 9 pages
http://dx.doi.org/10.1155/2012/401562
Research Article

Numerical Method for a Markov-Modulated Risk Model with Two-Sided Jumps

School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Received 24 August 2012; Accepted 30 October 2012

Academic Editor: Xinguang Zhang

Copyright © 2012 Hua Dong and Xianghua Zhao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper considers a perturbed Markov-modulated risk model with two-sided jumps, where both the upward and downward jumps follow arbitrary distribution. We first derive a system of differential equations for the Gerber-Shiu function. Furthermore, a numerical result is given based on Chebyshev polynomial approximation. Finally, an example is provided to illustrate the method.