Journal of Applied Mathematics
Volume 2012 (2012), Article ID 286792, 7 pages
Research Article

Ruin Probability in Compound Poisson Process with Investment

School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China

Received 1 February 2012; Accepted 29 March 2012

Academic Editor: Shiping Lu

Copyright © 2012 Yong Wu and Xiang Hu. 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.


We consider that the surplus of an insurer follows compound Poisson process and the insurer would invest its surplus in risky assets, whose prices satisfy the Black-Scholes model. In the risk process, we decompose the ruin probability into the sum of two ruin probabilities which are caused by the claim and the oscillation, respectively. We derive the integro-differential equations for these ruin probabilities these ruin probabilities. When the claim sizes are exponentially distributed, third-order differential equations of the ruin probabilities are derived from the integro-differential equations and a lower bound is obtained.