Optimal investment and reinsurance problem for the insurer's and the reinsurer's interests under default risk

This paper considers an optimal investment and reinsurance problem involving a defaultable security for a group which holds shares of an insurance company and a reinsurance company. Assuming that the claim process is described by a Brownian motion with drift, the insurer can purchase proportional reinsurance and invest a risk-free asset, a stock and a defaultable bond, and the reinsurer can invest a risk-free asset and a stock. Taking both the insurer and the reinsurer into account, this paper aims to maximize the expected product of the insurer's and the reinsurer's exponential utilities of terminal wealth. By using the techniques of stochastic control theory, the corresponding Hamilton-Jacobi-Bellman (HJB) equations are established for the pre-default case and post-default case, respectively. In both cases, closed-form expressions for the optimal strategies and the corresponding value functions are derived. Finally, numerical examples are given to illustrate the effects of model parameters on the optimal investment and reinsurance strategies, and the corresponding economic explanations are given. © 2020, Editorial Board of Journal of Systems Engineering Society of China. All right reserved.