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

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  • Masaaki Fujii
  • Akihiko Takahashi

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 flow of sales-and-purchase orders in the exchange market, where a large number of agents 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 a good 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. We also extend 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.

Suggested Citation

  • Masaaki Fujii & Akihiko Takahashi, 2020. "A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition," Papers 2003.03035, arXiv.org, revised Sep 2021.
    • Handle: RePEc:arx:papers:2003.03035
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Guanxing Fu & Ulrich Horst, 2018. "Mean-Field Leader-Follower Games with Terminal State Constraint," Papers 1809.04401, arXiv.org.
    5. Fu, Guanxing & Horst, Ulrich, 2018. "Mean-Field Leader-Follower Games with Terminal State Constraint," Rationality and Competition Discussion Paper Series 129, CRC TRR 190 Rationality and Competition.
    6. Olivier Guéant & Jean-Michel Lasry & Pierre Louis Lions, 2010. "Mean Field Games and Oil Production," Post-Print hal-01393104, HAL.
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    Cited by:

    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. 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.
    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. Masaaki Fujii & Akihiko Takahashi, 2020. "Strong Convergence to the Mean-Field Limit of A Finite Agent Equilibrium," Papers 2010.09186, arXiv.org, revised Dec 2021.

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