研究了两个风险厌恶的竞争的机构投资者之间的离散时间最优投资选择博弈模型, 每个机构投资者都考虑其竞争对手的相对业绩. 机构投资者可以投资于相同的无风险资产和不同的具有相关关系的风险股票, 以反映投资的资产专门化. 机构投资者选择动态投资策略使得终端绝对财富和相对财富的加权和的期望效用最大. 首先, 定义了Nash均衡投资策略. 其次, 在资产专门化和机构投资者具有指数效用函数下, 得到了Nash均衡投资策略和值函数的显示表达式, 分析了机构投资者之间的竞争对Nash均衡投资策略和值函数的影响. 然后, 在资产分散化和股票的收益率服从正态分布下, 得到了Nash均衡投资策略和值函数的显示表达式, 给出了Nash均衡投资策略和值函数与模型主要参数之间的关系. 最后, 通过数值计算给出了机构投资者采取专门化投资策略, 还是分散化投资策略的条件. 结果表明机构投资者之间的竞争会影响其对风险的承担, 投资机会集对机构投资者的Nash均衡投资策略和值函数会产生很大的影响.

In this paper we study a discrete time multi-period optimal portfolio selection game problem between two risk-averse institutional investors when each investor takes into account his relative performance by comparison to his competitor. Both investors can invest freely in the risk-free asset and only one of the two correlated risky stocks is available to each investor, reflecting asset specialization. Each investor chooses a dynamic portfolio strategy to maximize his expected terminal utility of the weight sum of his wealth and the difference between his wealth and that of his competitor. We first characterize explicitly the unique Nash equilibrium portfolio strategies. Secondly, the Nash equilibrium portfolio strategy and the value function of each investor are obtained in closed forms for the case of each investor with an exponential utility function. The effects of the relative performance on the Nash equilibrium portfolio strategy and the value function are also analyzed. Furthermore, we obtain the closed-form expressions of the Nash equilibrium portfolio strategy and the value function under that the compounded return of two risky stocks are normally distributed and asset diversification. Sensitivity analysis is also provided to illustrate how the Nash equilibrium portfolio strategy and the value function change when some model parameters vary. Finally, the setting with and without asset specialization is analyzed by numerical examples. The results reveal that competition can change the institutional investor risk taking. Different investment possibilities may greatly influence the Nash equilibrium portfolio strategy and the value function of the institutional investor.