Discussion Papers 2021
CIRJE-F-1180 | "Strong Convergence to the Mean-Field Limit of A Finite Agent Equilibrium" |
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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 |
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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 |