The optimal investment problem for an insurer and a reinsurer under the constant elasticity of variance model

This paper focuses on an optimal management problem for a general insurance company which contains an insurer and a reinsurer. The general company aims to maximize the expected exponential utility of the weighted sum of the insurer's and the reinsurer's terminal wealth. In our model, the basic claim process is assumed to follow a Brownian motion with drift. The insurer and the reinsurer are allowed to invest in a risk-free asset and a risky asset, respectively. The prices of risky assets are described by the constant elasticity of variance (CEV) models. In addition, the insurer can purchase proportional reinsurance from the reinsurer. By solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation, we derive the optimal reinsurance and investment strategies for the insurer and the reinsurer, respectively. Finally, numerical simulations are presented to show the effects of model parameters on the optimal reinsurance and investment strategies.