Discussion Papers 2020

CIRJE-F-1144 "A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition"
Author Name

Fujii, Masaaki and Akihiko Takahashi

Date March 2020
Full Paper PDF file
Remarks

Published in SIAM Journal on Control and Optimization, Vol.60, No.1, 9, 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 sales-and-purchase orders in the exchange market, where a large number of agent 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.