Stochastic Differential Financial Portfolio Game Under CEV Model with CRRA Utility

This paper investigates a stochastic differential portfolio game between two competing investors with relative wealth preferences. The financial market consists of one risk-free asset and one risky asset, whose price dynamics follow the CEV model. We formulate this game as two utility maximization problems, where each investor aims to maximize their relative utility defined as the weighted average of the ratio between their terminal wealth and the competitor’s terminal wealth. Firstly, we derive the Hamilton–Jacobi–Bellman (HJB) equations and corresponding value functions through the dynamic programming principle. Next, we obtain the explicit solutions to equilibrium investment strategies and value functions for the non-zero-sum game under the CRRA utility framework. Finally, we conducted numerical simulations to analyze the impacts of model parameters on equilibrium strategies and provide relevant economic explanations.