Time-consistent investment-reinsurance strategy for mean-variance insurers with a defaultable security

This paper considers an optimal investment and reinsurance problem involving a defaultable security for an insurer under the mean-variance criterion in a jump diffusion risk model. The insurer can purchase proportional reinsurance or acquire new insurance business and invest in a financial market consisting of a risk-free asset, a stock and a defaultable bond. In particular, the correlation between the insurance risk model and the financial market is also considered. From a game theoretic perspective, the extended Hamilton-Jacobi-Bellman systems of equations are established for the post-default case and the pre-default case, respectively. In both cases, closed-form expressions for the optimal time-consistent investment reinsurance strategies and the corresponding value functions are derived. Moreover, some properties of optimal strategies, value functions and efficient frontiers are discussed either analytically or numerically. (C) 2016 Elsevier Inc. All rights reserved.