Hawkes-Based Optimal Investment and Reinsurance Strategies for Loss-Averse Insurer

This paper studies an optimal reinsurance and investment problem for a kind of loss-averse Insurer. Considering that claim events are clustered, this paper adopts Hawkes processes to describe the claim numbers and establishes Hawkes risk model. Insurer is assumed to operate two different classes of insurance businesses, the reinsurance strategies are studied according to the different decay intensities of the claim number processes. In this paper, we assume that the insurer’s goal is to maximize the expected S-shaped utility from the terminal wealth. And explicit solutions of optimal investment and proportional reinsurance strategies are given by martingale approach. Finally, the influence of the main parameters of the model on the optimal strategies is discussed by numerical analysis. In addition, when the claim events are clustered, the higher the claim risk faced by insurer. In this situation, the insurer will buy the more expensive reinsurance to reduce his claim risk.