Abstract: This paper studies a stochastic differential portfolio game between two investors under the Heston model. The financial market is constituted by a risk-free asset and a risky asset whose price process is subjected to the Heston model. The game is formulated by two utility maximization problems, and each investor tries to maximize his utility of the difference between his terminal wealth and that of his competitor. Firstly, we derive the HJB equations and the corresponding value functions by using the dynamic programming principle. Then, the explicit expressions of equilibrium investment strategies and the value functions for the non-zero game under the framework of the power utility function are received. Finally, the influence of the model parameters on the equilibrium investment strategies and value functions is obtained by numerical simulation. Thus, a certain theory instruction for the actual assets and liabilities management is provided.

Key words: portfolio game, Heston model, liability, Nash equilibrium

摘要： 本文研究了Heston随机波动模型下两个投资人之间的随机微分投资组合博弈问题。假设金融市场上存在价格过程服从常微分方程的无风险资产和价格过程服从Heston随机波动率模型的风险资产。该博弈问题被构造成两个效用最大化问题,每个投资者的目标是最大化终止时刻个人财富与竞争对手财富差的效用。首先,我们应用动态规划原理,得出了相应值函数所满足的HJB方程。然后,得到了在幂期望效用框架下非零和博弈的均衡投资策略和值函数的显式表达。最后,借助数值模拟,分析了模型中的参数对均衡投资策略和值函数的影响,从而为资产负债管理提供一定的理论指导。

关键词: 投资组合博弈, Heston模型, 负债, 纳什均衡