AI 中文总结
研究N主体博弈中的最优消费-投资问题，利用随机最大值原理刻画平均场均衡，通过数值实验说明结果及金融含义，还基于此构建N主体博弈的近似纳什均衡。
AI 中文摘要
本文研究了N主体博弈中的最优消费-投资问题及其相关平均场博弈。每个主体投资于受个体噪声、共同噪声和向下跳跃风险影响的单个风险资产，主体间的相互作用由消费和终端财富中的相对业绩考量引发。在平均场极限下，利用随机最大值原理以解析形式刻画了确定性平均场均衡。给出数值实验说明所得均衡及其金融含义。最后基于平均场均衡为N主体博弈构建了近似纳什均衡。该模型受[参考文献]启发。
英文摘要
This paper studies an optimal consumption--investment problem for competitive agents in an \(N\)-player game and its associated mean field game. Each agent invests in an individual risky asset subject to idiosyncratic noise, common noise and downward jump risk, and the interaction among agents is induced by relative performance concerns in both consumption and terminal wealth. In the mean field limit, we characterize a deterministic mean field equilibrium in analytical form by using the stochastic maximum principle. Numerical experiments are presented to illustrate the resulting equilibrium and its financial implications. Finally, based on the obtained mean field equilibrium, we construct an approximate Nash equilibrium for the \(N\)-player game. This model is motivated by \cite{Merton1971} and \cite{Lacker2020}.
