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

Author

Listed:
  • Masaaki Fujii

    (Graduate School of Economics, The University of Tokyo)

  • Akihiko Takahashi

    (Graduate School of Economics, The University of Tokyo)

Abstract

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.

Suggested Citation

  • 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.
    • Handle: RePEc:tky:fseres:2021cf1180
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    References listed on IDEAS

    as
    1. 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.
    2. Kim Weston & Gordan Žitković, 2020. "An incomplete equilibrium with a stochastic annuity," Finance and Stochastics, Springer, vol. 24(2), pages 359-382, April.
    3. Olivier Féron & Peter Tankov & Laura Tinsi, 2020. "Price Formation and Optimal Trading in Intraday Electricity Markets with a Major Player," Risks, MDPI, vol. 8(4), pages 1-21, December.
    4. Masaaki Fujii & Akihiko Takahashi, 2020. "A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition," CARF F-Series CARF-F-473, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    5. Charles-Albert Lehalle & Charafeddine Mouzouni, 2019. "A mean field game of portfolio trading and its consequences on perceived correlations," Working Papers hal-02003143, HAL.
    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. Li, Juan & Wei, Qingmeng, 2014. "Lp estimates for fully coupled FBSDEs with jumps," Stochastic Processes and their Applications, Elsevier, vol. 124(4), pages 1582-1611.
    8. 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.
    9. Masaaki Fujii & Akihiko Takahashi, 2020. "A Finite Agent Equilibrium in an Incomplete Market and its Strong Convergence to the Mean-Field Limit," CIRJE F-Series CIRJE-F-1156, CIRJE, Faculty of Economics, University of Tokyo.
    10. Masaaki Fujii, 2019. "Probabilistic Approach to Mean Field Games and Mean Field Type Control Problems with Multiple Populations," CIRJE F-Series CIRJE-F-1133, CIRJE, Faculty of Economics, University of Tokyo.
    11. Masaaki Fujii & Akihiko Takahashi, 2020. "A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition," CIRJE F-Series CIRJE-F-1144, CIRJE, Faculty of Economics, University of Tokyo.
    12. Olivier F'eron & Peter Tankov & Laura Tinsi, 2020. "Price formation and optimal trading in intraday electricity markets with a major player," Papers 2011.07655, arXiv.org.
    13. Xing, Hao & Žitković, Gordan, 2018. "A class of globally solvable Markovian quadratic BSDE systems and applications," LSE Research Online Documents on Economics 73440, London School of Economics and Political Science, LSE Library.
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