Optimal investment and reinsurance strategies for insurers with generalized mean–variance premium principle and no-short selling

Abstract

This paper analyzes the optimal investment and reinsurance strategies for insurers with a generalized mean–variance premium principle. The surplus process of the insurer is described by the diffusion model which is an approximation of the classical Cramér–Lundberg model. The insurer can purchase reinsurance and invest her surplus in a financial market consisting of a risk-free asset and multiple risky assets. The insurer is not allowed to short sell the risky assets. Two optimization problems, maximizing the expected utility function of terminal wealth and minimizing the probability of ruin, are considered. We first derive the form of optimal reinsurance for the two optimization problems. Then, by using the stochastic dynamic programming, we obtain the closed-form expressions of optimal investment and reinsurance strategies and optimal value functions for the two optimization problems. We find that our results are more general than some ones in the existing literature.