Discussion Papers 2020
CIRJE-F-1156 | "A Finite Agent Equilibrium in an Incomplete Market and its Strong Convergence to the Mean-Field Limit" |
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Author Name | Fujii, Masaaki and Akihiko Takahashi |
Date | October 2020 |
Full Paper | |
Remarks | Published in SSRN Electronic Journal, December 2020. |
Abstract |
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We investigate the problem of equilibrium price formation in an incomplete securities market. Each financial firm (agent) tries to minimize its cost via continuous-time trading with a securities exchange while facing the systemic and idiosyncratic noises as well as the stochastic order- ows from its over-the-counter clients. We have shown, in the accompanying paper (Fujii & Takahashi) [19], that the solution to a certain forward backward stochastic differential equation of conditional McKean-Vlasov type gives a good approximate of the equilibrium price which clears the market in the large population limit. In this work, we prove the existence of a unique market clearing equilibrium among the heterogeneous agents of finite population size. We show the strong convergence to the corresponding mean-field limit given in [19] under suitable conditions. In particular, we provide the stability relation between the market clearing price for the heterogeneous agents and that for the homogeneous mean-field limit. |