Time-consistent reinsurance-investment strategies for insurer and reinsurer under jump-diffusion and volatility risks

This paper studies the time-inconsistent optimal reinsurance-investment problem with the joint interests of an insurer and a reinsurer under the jump-diffusion and Heston models. We aim to find the optimal strategy to maximize the sum of weighted wealth of the insurer and reinsurer under the mean-variance framework. By applying dynamic programming and differential game theories, we give the Hamilton-Jacobi-Bellman (HJB) equation and verification theorem. Then, the closed-form solutions of optimal strategies and the value functions are obtained. Moreover, the sensitivity analysis is carried out.