Stochastic Non‐Zero Differential Game Between Two Insurers Under CEV (E‐CEV) Model

This paper considers a stochastic non‐zero‐sum differential game between two competitive insurers. Both insurers are allowed to invest in one risk‐free asset and one risky asset, whose price dynamics follow the constant elasticity of variance (CEV) model, specifically the extended CEV (E‐CEV) model. At the same time, they are permitted to purchase proportional reinsurance to control the risks associated with individual claims. The goal of each insurer is to determine optimal strategies that maximize the expected utility of terminal wealth relative to that of their competitor. The Nash equilibrium reinsurance and investment strategies are explicitly derived using stochastic control theory techniques. Finally, we numerically examine the effect of model parameters on optimal investment and reinsurance strategies.