Optimal investment problem with multiple risky assets and correlation between risk model and financial market for an insurer under the CEV model

This article investigates the optimal investment problem with multiple risky assets and the correlation between risk model and financial market for an insurer. The insurer’s claim process is described by a Brownian motion with drift under the mean-variance premium principle. The insurer is allowed to invest in one risk-free asset and multiple risky assets whose price processes follow the constant elasticity of variance (CEV) model. Moreover, the correlation between the claim process and each risky asset’s price is taken into account. The insurer’s objective is to maximize the exponential utility of the terminal wealth. By applying dynamic programming approach, we propose a new form of the solution to the Hamilton-Jacobi-Bellman (HJB) equation and derive the optimal investment strategy explicitly. This is the first time that an explicit result of the optimal investment strategy is given under the framework of the exponential utility function for the general CEV model based on the correlation between the financial market and the insurance market. In addition, we provide some special cases of our model, i.e., the optimal investment problem with one risky asset and that with two risky assets. We also consider the case that the risk model and the financial market is independent. The results show that ignoring the correlation between the claim process and the risky asset’s price will misestimate the value of risky assets and has a significant effect on the insurer’s investment decision. Finally, numerical simulations are presented to analyze the effects of model parameters on the optimal investment strategy.