A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition

Masaaki Fujii and Akihiko Takahashi

Papers from arXiv.org

Abstract: In this work, we study an equilibrium-based continuous asset pricing problem which seeks to form a price process endogenously by requiring it to balance the flow of sales-and-purchase orders in the exchange market, where a large number of agents are interacting through the market price. Adopting a mean field game (MFG) approach, we find a special form of forward-backward stochastic differential equations of McKean-Vlasov type with common noise whose solution provides a good approximate of the market price. We show the convergence of the net order flow to zero in the large N-limit and get the order of convergence in N under some conditions. We also extend the model to a setup with multiple populations where the agents within each population share the same cost and coefficient functions but they can be different population by population.

Date: 2020-03, Revised 2021-09
New Economics Papers: this item is included in nep-gth
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