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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 579534, 9 pages
http://dx.doi.org/10.1155/2013/579534
Research Article

Randomized Dividends in a Discrete Insurance Risk Model with Stochastic Premium Income

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 23 January 2013

Academic Editor: Guangchen Wang

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

The compound binomial insurance risk model is extended to the case where the premium income process, based on a binomial process, is no longer a constant premium rate of 1 per period and insurer pays a dividend of 1 with a probability when the surplus is greater than or equal to a nonnegative integer . The recursion formulas for expected discounted penalty function are derived. As applications, we present the recursion formulas for the ruin probability, the probability function of the surplus prior to the ruin time, and the severity of ruin. Finally, numerical example is also given to illustrate the effect of the related parameters on the ruin probability.