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

TL;DR

This paper models equilibrium price formation in a market with one major and many minor firms, deriving the price process both for finite populations and in the mean field limit, considering stochastic trading and noise.

Contribution

It introduces a novel framework for equilibrium price formation with a major player and derives the mean field limit of this model.

Findings

Derived the equilibrium price process in finite and infinite populations.

Characterized the functional form of the major firm's price impact.

Established the connection between finite market models and their mean field limits.

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.