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Journal of Applied Mathematics
Volume 2014, Article ID 717269, 12 pages
http://dx.doi.org/10.1155/2014/717269
Research Article

On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes

1College of Business Administration, Hunan University, Changsha 410082, China
2College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, China
3School of Mathematical Sciences, Nankai University, Tianjin 300071, China

Received 19 December 2013; Accepted 17 January 2014; Published 5 March 2014

Academic Editor: Yansheng Liu

Copyright © 2014 Huiming Zhu 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 focus on the expected discounted penalty function of a compound Poisson risk model with random incomes and potentially delayed claims. It is assumed that each main claim will produce a byclaim with a certain probability and the occurrence of the byclaim may be delayed depending on associated main claim amount. In addition, the premium number process is assumed as a Poisson process. We derive the integral equation satisfied by the expected discounted penalty function. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the expected discounted penalty function is derived. Finally, for the exponential claim sizes, we present the explicit formula for the expected discounted penalty function.