Strong Convergence to the Mean-Field Limit of A Finite Agent Equilibrium

TL;DR

This paper proves that a finite agent equilibrium in a securities market converges strongly to its mean-field limit as the number of agents grows large, providing explicit estimates on price differences.

Contribution

It establishes the existence of finite agent equilibria and their strong convergence to the mean-field limit, extending previous asymptotic results.

Findings

Strong convergence of finite agent equilibrium to mean-field limit

Explicit estimates on equilibrium price differences

Existence of finite agent equilibrium under suitable conditions

Abstract

We study an equilibrium-based continuous asset pricing problem for the securities market. 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; one consisting of heterogeneous agents of finite population size and the other of homogeneous agents of infinite population size.