Optimal investment strategies for an insurer and a reinsurer with a jump diffusion risk process under the CEV model

In this paper, we consider the optimal investment problem for both an insurer and a reinsurer. The insurer's wealth process is described by a jump diffusion risk model and the insurer can purchase proportional reinsurance from the reinsurer. Both the insurer and the reinsurer are allowed to invest in a risk-free asset and a risky asset whose price process follows the constant elasticity of variance (CEV) model. Moreover, the correlation between risk model and the risky asset's price is considered. The objective is maximizing the expected utility of the insurer's and the reinsurer's terminal wealth. Applying stochastic control theory, we establish the corresponding Hamilton-Jacobi-Bellman (HJB) equations and derive optimal investment-reinsurance strategies for exponential utility function. Finally, numerical examples are provided to analyze the effects of parameters on the optimal strategies.