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

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 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.