Optimal combining quota-share and excess of loss reinsurance to maximize the expected utility

Abstract

In this paper, from an insurer’s point of view, we consider the optimal combining quota-share and excess of loss reinsurance to maximize the expected exponential utility from terminal wealth. By stochastic control theory and the corresponding Hamilton-Jacobi-Bellman equation, we derive the closed form expressions of the optimal strategies and value function not only for the diffusion approximation risk model but also for the jump-diffusion risk model. We also conclude that, under some conditions, there exists a pure excess of loss reinsurance strategy which is better than any combinational reinsurance strategy.