提供了一个关于两个投资者之间非零和随机微分投资组合博弈问题的系统研究。假设投资者具有指数效用,金融市场上存在两种资产,风险资产服从常弹性方差模型。该非零和博弈问题被构造成两个效用最大化问题。每个投资者最大化终止时刻个人财富与他的竞争对手的财富的差的效用。通过动态规划方法,得到了价值函数满足的HJB方程、值函数以及最优投资均衡策略的显式表达式。最后进行了数值模拟,提供了均衡策略合理的经济解释。
In this paper, we consider a systematic non-zero-sum stochastic differential portfolio game problem between two investors. Each investor is assumed to have exponential utility. The financial market is assumed to consist of two financial assets. In addition, the dynamics of risky asset is modeled by a constant elasticity of variance model. Furthermore, we formulate the non-zero-sum game as two utility maximization problems. Each investor is assumed to maximize his utility of the difference between his terminal wealth and that of his competitor. By using dynamic programming, we derive the HJB equation for the value function. Meanwhile, we obtain the closed-form solution to the value function and Nash equlibrium for portfolio decision. Finally, we provide numerical simulation together with sund economic implications.