Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 320146, 9 pages
http://dx.doi.org/10.1155/2013/320146
Research Article

On the Expected Discounted Penalty Function for a Markov Regime-Switching Insurance Risk Model with Stochastic Premium Income

Wenguang Yu1,2

1School of Mathematics, Shandong University, Jinan 250100, China
2School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China

Received 3 December 2012; Accepted 30 January 2013

Academic Editor: Fuyi Xu

Copyright © 2013 Wenguang Yu. 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

We consider a Markovian regime-switching risk model (also called the Markov-modulated risk model) with stochastic premium income, in which the premium income and the claim occurrence are driven by the Markovian regime-switching process. The purpose of this paper is to study the integral equations satisfied by the expected discounted penalty function. In particular, the discount interest force process is also regulated by the Markovian regime-switching process. Applications of the integral equations are given to be the Laplace transform of the time of ruin, the deficit at ruin, and the surplus immediately before ruin occurs. For exponential distribution, the explicit expressions for these quantities are obtained. Finally, a numerical example is also given to illustrate the effect of the related parameters on these quantities.