Optimal Proportional Reinsurance and Ruin Probability

Abstract

In this paper, we consider optimal proportional reinsurance from an insurer's point of view to maximize the adjustment coefficient. We obtain the explicit expressions for the optimal results in the diffusion approximation case as well as in the jump-diffusion case. Further, we derive a sharper bound on the ruin probability. When the claim sizes are exponentially distributed, we can prove that the Lundberg's inequality also holds for the ruin probability in the diffusion approximation case. Some numerical examples are presented to show that the ruin probability in the diffusion approximation case sometimes underestimates the ruin probability.

Keywords:

• Adjustment coefficient
• Diffusion approximation
• Jump-diffusion
• Proportional reinsurance
• Ruin probability

Mathematics Subject Classification:

• 62P05
• 91B30

ACKNOWLEDGMENTS

This research was supported by the National Natural Science Foundation of China (Grant no. 10571092). The authors would like to thank the anonymous referee, editor, and professor Peter Taylor, for their careful reading and helpful comments on an earlier version of this paper, which led to a considerable improvement of the presentation of the work.