Discussion Papers 2021

CIRJE-F-1180	"Strong Convergence to the Mean-Field Limit of A Finite Agent Equilibrium"
Author Name	Fujii, Masaaki and Akihiko Takahashi
Date	December 2021
Full Paper	PDF file
Remarks	Published in SIAM Journal on Financial Mathematics, Vol.13, Iss.2, 2022.

Abstract
We study an equilibrium-based continuous asset pricing problem for the securities mar- ket. In the previous work [16], we have shown that a certain price process, which is given by the solution to a forward backward stochastic differential equation of conditional McKean- Vlasov type, asymptotically clears the market in the large population limit. In the current work, under suitable conditions, we show the existence of a finite agent equilibrium and its strong convergence to the corresponding mean-field limit given in [16]. As an important byproduct, we get the direct estimate on the difference of the equilibrium price between the two markets; the one consisting of heterogeneous agents of finite population size and the other of homogeneous agents of infinite population size.
Keywords: mean field games, equilibrium in incomplete markets, common noise, market clearing, price formation

Abstract

We study an equilibrium-based continuous asset pricing problem for the securities mar- ket. In the previous work [16], we have shown that a certain price process, which is given by the solution to a forward backward stochastic differential equation of conditional McKean- Vlasov type, asymptotically clears the market in the large population limit. In the current work, under suitable conditions, we show the existence of a finite agent equilibrium and its strong convergence to the corresponding mean-field limit given in [16]. As an important byproduct, we get the direct estimate on the difference of the equilibrium price between the two markets; the one consisting of heterogeneous agents of finite population size and the other of homogeneous agents of infinite population size.

Keywords: mean field games, equilibrium in incomplete markets, common noise, market clearing, price formation