Discussion Papers 2021
CIRJE-F-1177 | "A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition" |
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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 |
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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 |