Non-zero-sum reinsurance and investment game with correlation between insurance market and financial market under CEV model

Abstract

<p style='text-indent:20px;'>In this paper, we study a non-zero-sum investment and reinsurance game for two insurers. Each insurer's surplus process is described by a Brownian motion with drift. Both insurers are allowed to purchase proportional reinsurance and invest in a risk-free asset and a risky asset. The price process of the risky asset follows the constant elasticity of variance (CEV) model, and the correlation between the risky asset's price process and the claim process is considered. Each insurer aims to maximize the expected exponential utility of his terminal wealth relative to that of his competitor. By applying stochastic control theory, we establish the corresponding Hamilton-Jacobi-Bellman (HJB) equation and derive optimal investment-reinsurance strategies for two insurers under exponential utility function. Furthermore, we consider the insurer's optimal investment-reinsurance strategies without competition. Finally, numerical analyses are provided to analyze the effects of model parameters on the optimal strategies.</p>