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

Masaaki Fujii and Akihiko Takahashi
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Masaaki Fujii: Quantitative Finance Course, Graduate School of Economics, The University of Tokyo
Akihiko Takahashi: Quantitative Finance Course, Graduate School of Economics, The University of Tokyo

No CARF-F-529, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

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; the one consisting of heterogeneous agents of finite population size and the other of homogeneous agents of infinite population size.

Pages: 33
Date: 2021-12
New Economics Papers: this item is included in nep-gth
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