Mean-Field Price Formation on Trees

Masaaki Fujii
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Masaaki Fujii: Graduate School of Economics, The University of Tokyo

No CARF-F-606, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

Abstract: In this work, we combine the mean-fi eld 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.

Pages: 29
Date: 2025-10
New Economics Papers: this item is included in nep-upt
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