Minimization of ruin probability with joint strategies of investment and reinsurance

Abstract

We investigate the problem of minimizing ruin probability by joint decisions of excess-of-loss reinsurance and investment in a financial market. The insurer’s reserve is modeled by a diffusion process and may be invested in a financial market consisting of a risky asset with the price process following the geometric Brownian motion and a risk-free asset with a fixed return rate. Borrowing is allowed, but with an interest rate higher than the interest rate of the risk-free investment. Meanwhile, an excess-of-loss reinsurance may be purchased to alleviate the risk of ruin. We apply stochastic control theory and find the optimal strategy of joint reinsurance and investment decisions, and derive the closed form expression of the minimum ruin probability function. Results are illustrated numerically.

Keywords:

• Risk process
• ruin probability
• excess-of-loss reinsurance
• stochastic control
• Hamilton-Jacobi-Bellman (HJB) equation

Acknowledgment

The authors thank an anonymous reviewer for constructive criticisms and very helpful comments. Xikui Wang acknowledges funding from the Natural Sciences and Engineering Research Council of Canada.

Additional information

Funding

The authors thank an anonymous reviewer for constructive criticisms and very helpful comments. Xikui Wang acknowledges funding from the Natural Sciences and Engineering Research Council of Canada.