Minimizing the risk of absolute ruin under a diffusion approximation model with reinsurance and investment

Abstract

This paper studies the optimization problem with both investment and proportional reinsurance control under the assumption that the surplus process of an insurance entity is represented by a pure diffusion process. The company can buy proportional reinsurance and invest its surplus into a Black-Scholes risky asset and a risk free asset without restrictions. The authors define absolute ruin as that the liminf of the surplus process is negative infinity and propose absolute ruin minimization as the optimization scenario. Applying the HJB method the authors obtain explicit expressions for the minimal absolute ruin function and the associated optimal investment strategy. The authors find that the minimal absolute ruin function here is convex, but not S-shaped investigated by Luo and Taksar (2011). And finally, from behavioral finance point of view, the authors come to the conclusion: It is the restrictions on investment that results in the kink of minimal absolute ruin function.