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

Masaaki Fujii and Akihiko Takahashi

Papers from arXiv.org

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.

Date: 2020-10, Revised 2021-12
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