Optimal time-consistent investment and reinsurance strategies for meanヨvariance insurers with state dependent risk aversion

In this paper, we study an insurer’s optimal time-consistent strategies under themean–variance criterion with state dependent risk aversion. It is assumed that the surplus process is approximated by a diffusion process. The insurer can purchase proportional reinsurance and invest in a financial market which consists of one risk-free asset andmultiple risky assets whose price processes follow geometric Brownian motions. Under these, we consider two optimization problems, an investment–reinsurance problem and an investment-only problem. In particular, when the risk aversion depends dynamically on current wealth, the model is more realistic. Using the approach developed by Björk and Murgoci (2009), the optimal time-consistent strategies for the two problems are derived bymeans of corresponding extension of the Hamilton–Jacobi–Bellman equation. The optimal time-consistent strategies are dependent on current wealth, this case thus is more reasonable than the one with constant risk aversion. © 2013 Elsevier B.V. All rights reserved.