We analyze a family of portfolio management problems under relative performance criteria, for fund managers having CARA or CRRA utilities and trading in a common investment horizon in log‐normal markets. We construct explicit constant equilibrium strategies for both the finite population games and the corresponding mean field games, which we show are unique in the class of constant equilibria. In the CARA case, competition drives agents to invest more in the risky asset than they would otherwise, while in the CRRA case competitive agents may over‐ or underinvest, depending on their levels of risk tolerance.

中文翻译：

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在相对绩效标准下进行最优投资的平均场和n代理博弈

对于具有CARA或CRRA公用事业并在对数正态市场中具有共同投资视野的交易的基金经理，我们根据相对绩效标准分析了一系列投资组合管理问题。我们为有限的总体博弈和相应的均值场博弈构建了显式的恒定均衡策略，这些策略在恒定均衡类中是唯一的。在CARA案例中，竞争驱使代理商在风险资产上进行的投资要多于其他方式，而在CRRA案例中，竞争代理商可能根据其风险承受能力的水平进行过度投资或投资不足。