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A Finite Agent Equilibrium in an Incomplete Market and its Strong Convergence to the Mean-Field Limit

Author

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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)

Abstract

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-flows 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.

Suggested Citation

  • Masaaki Fujii & Akihiko Takahashi, 2020. "A Finite Agent Equilibrium in an Incomplete Market and its Strong Convergence to the Mean-Field Limit," CARF F-Series CARF-F-495, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf495
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    References listed on IDEAS

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    Cited by:

    1. Masaaki Fujii & Akihiko Takahashi, 2021. "Equilibrium Price Formation with a Major Player and its Mean Field Limit," CARF F-Series CARF-F-509, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Masaaki Fujii & Akihiko Takahashi, 2022. "Equilibrium Price Formation with a Major Player and its Mean Field Limit (Forthcoming in ESAIM: Control, Optimization and Calculus of Variations)(Revised version of CARF-F-509)," CARF F-Series CARF-F-533, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    3. Masaaki Fujii & Akihiko Takahashi, 2021. "A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition," CARF F-Series CARF-F-521, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    4. Masaaki Fujii & Akihiko Takahashi, 2021. "A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition," CIRJE F-Series CIRJE-F-1177, CIRJE, Faculty of Economics, University of Tokyo.
    5. Masaaki Fujii, 2020. "Probabilistic Approach to Mean Field Games and Mean Field Type Control Problems with Multiple Populations," CARF F-Series CARF-F-497, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    6. Masaaki Fujii & Akihiko Takahashi, 2021. "``Equilibrium Price Formation with a Major Player and its Mean Field Limit''," CIRJE F-Series CIRJE-F-1162, CIRJE, Faculty of Economics, University of Tokyo.
    7. Masaaki Fujii & Akihiko Takahashi, 2021. "Strong Convergence to the Mean-Field Limit of A Finite Agent Equilibrium," CIRJE F-Series CIRJE-F-1180, CIRJE, Faculty of Economics, University of Tokyo.
    8. Masaaki Fujii & Akihiko Takahashi, 2021. "Equilibrium Price Formation with a Major Player and its Mean Field Limit," Papers 2102.10756, arXiv.org, revised Feb 2022.

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