Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 802518, 26 pages
Research Article

Dynamic Proportional Reinsurance and Approximations for Ruin Probabilities in the Two-Dimensional Compound Poisson Risk Model

1School of Insurance and Economics, University of International Business and Economics, Beijing 100029, China
2School of Science, Hebei University of Technology, Tianjin 300130, China

Received 8 October 2012; Accepted 28 November 2012

Academic Editor: Xiaochen Sun

Copyright © 2012 Yan Li and Guoxin Liu. 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 the dynamic proportional reinsurance in a two-dimensional compound Poisson risk model. The optimization in the sense of minimizing the ruin probability which is defined by the sum of subportfolio is being ruined. Via the Hamilton-Jacobi-Bellman approach we find a candidate for the optimal value function and prove the verification theorem. In addition, we obtain the Lundberg bounds and the Cramér-Lundberg approximation for the ruin probability and show that as the capital tends to infinity, the optimal strategies converge to the asymptotically optimal constant strategies. The asymptotic value can be found by maximizing the adjustment coefficient.