具有竞争或同伦互动的伊藤扩散市场中的$N$ -局中人和平均场博弈
$N$-player and Mean-field Games in Itô-diffusion Markets with Competitive or Homophilous Interaction
摘要：
在伊藤扩散环境中，我们介绍和分析$N$的球员和共同噪声平均场游戏的背景下，在一个共同的市场中的最优投资组合选择。参与者在有限的范围内进行投资，并在竞争或同质性的驱动下进行互动。本文研究了一个不完全市场模型，其中参与者具有常数的个人风险容忍系数（CARA效用）。我们还考虑了一般情况下的随机个人风险容忍度和分析相关的游戏在一个完整的市场设置。这种随机性使问题变得更加复杂，因为它导致了（$N$或连续体）辅助的“个体"伊藤扩散市场。对于所有的情况下，我们得到明确的或封闭形式的解决方案的平衡随机过程，最佳状态过程，和游戏的价值。
英文摘要：
In Itô-diffusion environments, we introduce and analyze $N$-player and common-noise mean-field games in the context of optimal portfolio choice in a common market. The players invest in a finite horizon and also interact, driven either by competition or homophily. We study an incomplete market model in which the players have constant individual risk tolerance coefficients (CARA utilities). We also consider the general case of random individual risk tolerances and analyze the related games in a complete market setting. This randomness makes the problem substantially more complex as it leads to ($N$ or a continuum of) auxiliary ''individual'' Itô-diffusion markets. For all cases, we derive explicit or closed-form solutions for the equilibrium stochastic processes, the optimal state processes, and the values of the games.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
