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Abstract and Applied Analysis
Volume 2014, Article ID 730174, 7 pages
http://dx.doi.org/10.1155/2014/730174
Research Article

The Gerber-Shiu Expected Penalty Function for the Risk Model with Dependence and a Constant Dividend Barrier

1Department of Mathematics, Hunan University of Science and Technology, Xiangtan, Hunan 411201, China
2Department of Mathematics, Central South University, Changsha, Hunan 410075, China

Received 12 June 2014; Revised 11 July 2014; Accepted 11 July 2014; Published 23 July 2014

Academic Editor: Dumitru Baleanu

Copyright © 2014 Donghai Liu et al. 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 compound Poisson risk model with dependence and a constant dividend barrier. A dependence structure between the claim amount and the interclaim time is introduced through a Farlie-Gumbel-Morgenstern copula. An integrodifferential equation for the Gerber-Shiu discounted penalty function is derived. We also solve the integrodifferential equation and show that the solution is a linear combination of the Gerber-Shiu function with no barrier and the solution of an associated homogeneous integrodifferential equation.