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 endogenouslyboth in the market of finite population size and in the corresponding mean field limit.

Modifications of Evans Price Equilibrium Model

“…The issue of differentiating the produce in accordance with equilibrium prices in the manufacture (the model for the simultaneous search with partial depth) is given in [9]. In [4] the stock exchange activity and equilibrium price in the shares market are introduced. Functioning and unique features of the equilibrium price described for transportation networks with perfect competition are regarded in [7], and, under oligopoly, in [1].…”

Equilibrium pricing of securities in the co-presence of cooperative and non-cooperative populations

“…In [28], the same authors provide the FBSDE characterization of the market clearing price in the finite-agent market, and then prove its strong convergence to the mean-field model of [27]. Its extension to the presence of a major agent is studied in [29].…”

“…In this paper, we build upon the previous works [27][28][29] and develop a new model of a securities market composed of two populations of different types: the first one consists of cooperative agents, while the other one consists of non-cooperative agents. Every agent is supposed to be a registered financial firm trying to minimize her cost functional by the continuous trading at the common exchange.…”