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

CARF Working Paper CARF-F-473

24 Pages Posted: 31 Mar 2020

See all articles by Masaaki Fujii

Masaaki Fujii

University of Tokyo - Faculty of Economics

Akihiko Takahashi

University of Tokyo - Faculty of Economics

Date Written: March 6, 2020

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.

JEL Classification: G12, C61, C73

Suggested Citation

Fujii, Masaaki and Takahashi, Akihiko, A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition (March 6, 2020). CARF Working Paper CARF-F-473 , Available at SSRN: https://ssrn.com/abstract=3549733 or http://dx.doi.org/10.2139/ssrn.3549733

Masaaki Fujii (Contact Author)

University of Tokyo - Faculty of Economics ( email )

7-3-1 Hongo, Bunkyo-ku
Tokyo 113-0033
Japan

Akihiko Takahashi

University of Tokyo - Faculty of Economics ( email )

7-3-1 Hongo, Bunkyo-ku
Tokyo 113-0033
Japan

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
8
Abstract Views
140
PlumX Metrics