Optimal Excess-of-Loss Reinsurance and Investment in a Stock Market with Ornstein-Uhlenbeck Process

This paper studies the optimal investment and excess-of-loss reinsurance strategies in a diffusion approximation risk model. It is assumed that the insurance company can purchase excess-of-loss reinsurance and invest its reserve in a financial market composed of a risk-free asset and a risky asset. The price model of risky asset is influenced by an Ornstein-Uhlenbeck process. The goal of the insurance company is to maximize the expected exponential utility of the terminal wealth. Using stochastic control theory and HJB equation, the explicit expressions for optimal strategies and value function are derived. Finally, the influence of model parameters on the optimal strategy and value function is analyzed through numerical analysis.