Equilibrium Price Formation with a Major Player and its Mean Field Limit

Abstract

In this article, we consider the problem of equilibrium price formation in an incomplete securities market consisting of one major financial firm and a large number of minor firms. They carry out continuous trading via the securities exchange to minimize their cost while facing idiosyncratic and common noises as well as stochastic order flows from their individual clients. The equilibrium price process that balances demand and supply of the securities, including the functional form of the price impact for the major firm, is derived endogenously both in the market of finite population size and in the corresponding mean field limit.

A Random-Supply Mean Field Game Price Model

“…[20] obtained the equilibrium price using a market clearing condition and a forwardbackward system of the McKean--Vlasov type characterizing the optimal trading rate for the agents. The same authors studied in [21] a further extension that considers a major player in the market. The market price is characterized by the solution to a forward-backward stochastic differential equation (SDE) system and a market-clearing condition.…”