Optimal Reinsurance and Investment Strategy under the Influence of Unexpected Events

This paper studies an optimal time-consistent reinsurance and investment problem under the influence of unexpected events. An insurer operates n insurance businesses, and after being affected by the unexpected events, n insurance businesses have interaction, meanwhile, the insurance business and the price of risky asset also have interaction. For each type of insurance business, the insurer reduces the claim risk through reinsurance. In addition, the insurer also increases his wealth by investing in the financial market. The financial market consists of a risk-free asset and a risky asset, and the price of the risky asset satisfies a jump-diffusion process. The main research goal of this paper is to find an optimal time-consistent reinsurance and investment strategy so as to maximize the expected terminal wealth while minimizing the variance of the terminal wealth. By using the stochastic control and stochastic optimization techniques, we establish the extended Hamilton-Jacobi-Bellman (HJB) equation. Explicit solutions for the optimal time-consistent reinsurance and investment strategy as well as the corresponding value function are obtained by solving the extended HJB equation, and the economic significance of the optimal strategy is discussed theoretically. Finally, numerical experiments are conducted to illustrate the effects of unexpected events on the optimal time-consistent reinsurance and investment strategy, and some meaningful economic insights or implications are provided.