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A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition

Author

Listed:
  • Masaaki Fujii

    (Faculty of Economics, The University of Tokyo)

  • Akihiko Takahashi

    (Faculty of Economics, The University of Tokyo)

Abstract

In this work, we study an equilibrium-based continuous asset pricing problem which seeks to form a price process endogenously by requiring it to balance the ow of sale-and-purchase orders in the exchange market, where a large number of agents $1\leq i\leq N$ are interacting through the market price. Adopting a mean field game (MFG) approach, we find a special form of forward-backward stochastic differential equations of McKean-Vlasov type with common noise whose solution provides an approximate of the market price. We show the convergence of the net order flow to zero in the large N-limit and get the order of convergence in N under some conditions. An extension of the model to a setup with multiple populations, where the agents within each population share the same cost and coefficient functions but they can be different population by population, is also discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:tky:fseres:2021cf1177
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    References listed on IDEAS

    as
    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, 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.
    3. 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.
    4. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(3), pages 659-684.
    5. 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.
    6. Olivier Guéant & Jean-Michel Lasry & Pierre Louis Lions, 2010. "Mean Field Games and Oil Production," Post-Print hal-01393104, HAL.
    7. 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.
    8. Clémence Alasseur & Imen Ben Taher & Anis Matoussi, 2020. "An Extended Mean Field Game for Storage in Smart Grids," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 644-670, February.
    9. 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.
    10. Masaaki Fujii, 2019. "Probabilistic Approach to Mean Field Games and Mean Field Type Control Problems with Multiple Populations," CARF F-Series CARF-F-467, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    11. Charles-Albert Lehalle & Charafeddine Mouzouni, 2019. "A mean field game of portfolio trading and its consequences on perceived correlations," Working Papers hal-02003143, HAL.
    12. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
    13. 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.
    14. Alexander Schied & Tao Zhang, 2017. "A State-Constrained Differential Game Arising In Optimal Portfolio Liquidation," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 779-802, July.
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