Discussion Papers 2021

CIRJE-F-1177	"A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition"
Author Name	Fujii, Masaaki and Akihiko Takahashi
Date	September 2021
Full Paper	PDF file
Remarks	Revised Version of CIRJE-F-1144(2020) Published in SIAM Journal on Control and Optimization, Vol.60, No.1, 2022.

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 sale-and-purchase orders in the exchange market, where a large number of agents 1 ≤ i ≤ N 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 an 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. An extension of 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, is also discussed.
Keywords: FBSDE of McKean-Vlasov type, common noise, general equilibrium

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 sale-and-purchase orders in the exchange market, where a large number of agents 1 ≤ i ≤ N 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 an 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. An extension of 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, is also discussed.

Keywords: FBSDE of McKean-Vlasov type, common noise, general equilibrium