CARF-F-473|ファイナンス

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

#### Author

#### 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 1 ≤ *i* ≤ *N* are interacting through the market price. Adopting a mean fild 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.