标题： 平均场价格形成在树上 显示英文标题

标题： Mean-Field Price Formation on Trees

摘要： 在本工作中，我们将均值场博弈论与二叉树框架的经典思想相结合，该框架由Sharpe和Cox, Ross & Rubinstein开创，以解决股票的均衡价格形成问题。 对于具有指数效用和指数型递归效用的代理人，我们证明了唯一均值场均衡的存在性，并通过将其轨迹限制在二叉树上，推导出股票价格的均衡转移概率的显式公式。 除了股票价格路径外，代理人还面临依赖于无法对冲的共同因素和异质因素的随机终期负债和增量禀赋。 最后，我们提供数值示例来说明这些组成部分对均衡价格分布的定性影响。 显示英文摘要

摘要： In this work, we combine the mean-field game theory with the classical idea of binomial tree framework, pioneered by Sharpe and Cox, Ross & Rubinstein, to solve the equilibrium price formation problem for the stock. For agents with exponential utilities and recursive utilities of exponential type, we prove the existence of a unique mean-field equilibrium and derive an explicit formula for equilibrium transition probabilities of the stock price by restricting its trajectories onto a binomial tree. The agents are subject to stochastic terminal liabilities and incremental endowments, both of which are dependent on unhedgeable common and idiosyncratic factors, in addition to the stock price path. Finally, we provide numerical examples to illustrate the qualitative effects of these components on the equilibrium price distribution.