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Mean-Field Leader-Follower Games with Terminal State Constraint

Author

Listed:
  • Fu, Guanxing

    (HU Berlin)

  • Horst, Ulrich

    (HU Berlin)

Abstract

We analyze linear McKean-Vlasov forward-backward SDEs arising in leader-follower games with mean-field type control and terminal state constraints on the state process. We establish an existence and uniqueness of solutions result for such systems in time-weighted spaces as well as a convergence result of the solutions with respect to certain perturbations of the drivers of both the forward and the backward component. The general results are used to solve a novel single-player model of portfolio liquidation under market impact with expectations feedback as well as a novel Stackelberg game of optimal portfolio liquidation with asymmetrically informed players.

Suggested Citation

  • 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.
    • Handle: RePEc:rco:dpaper:129
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    References listed on IDEAS

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    1. Graewe, Paulwin & Horst, Ulrich & Séré, Eric, 2018. "Smooth solutions to portfolio liquidation problems under price-sensitive market impact," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 979-1006.
    2. Paulwin Graewe & Ulrich Horst, 2016. "Optimal Trade Execution with Instantaneous Price Impact and Stochastic Resilience," Papers 1611.03435, arXiv.org, revised Jul 2017.
    3. Ulrich Horst & Jinniao Qiu & Qi Zhang, 2014. "A Constrained Control Problem with Degenerate Coefficients and Degenerate Backward SPDEs with Singular Terminal Condition," Papers 1407.0108, arXiv.org, revised Jul 2015.
    4. Paulwin Graewe & Ulrich Horst & Jinniao Qiu, 2013. "A Non-Markovian Liquidation Problem and Backward SPDEs with Singular Terminal Conditions," Papers 1309.0461, arXiv.org, revised Jan 2015.
    5. Kruse, T. & Popier, A., 2016. "Minimal supersolutions for BSDEs with singular terminal condition and application to optimal position targeting," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2554-2592.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Masaaki Fujii, 2022. "Equilibrium Pricing of Securities in the Co-presence of Cooperative and Non-cooperative Populations," CARF F-Series CARF-F-545, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. 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.
    3. 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.
    4. 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.
    5. Masaaki Fujii, 2022. "Equilibrium pricing of securities in the co-presence of cooperative and non-cooperative populations," Papers 2209.12639, arXiv.org, revised Jun 2023.
    6. 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.
    7. 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.
    8. Guanxing Fu & Xizhi Su & Chao Zhou, 2020. "Mean Field Exponential Utility Game: A Probabilistic Approach," Papers 2006.07684, arXiv.org, revised Jul 2020.
    9. Masaaki Fujii, 2022. "Equilibrium Pricing of Securities in the Co-Presence of Cooperative and Non-Cooperative Populations," CIRJE F-Series CIRJE-F-1201, CIRJE, Faculty of Economics, University of Tokyo.
    10. 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.
    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. David Evangelista & Yuri Thamsten, 2020. "On finite population games of optimal trading," Papers 2004.00790, arXiv.org, revised Feb 2021.
    13. 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.
    14. 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.
    15. 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.
    16. Masaaki Fujii, 2023. "Equilibrium pricing of securities in the co-presence of cooperative and non-cooperative populations (Forthcoming in ESAIM: Control, Optimisation and Calculus of Variations) (Revised version of CARF-F-," CARF F-Series CARF-F-562, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    17. 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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    More about this item

    Keywords

    mean-field control; stackelberg game; mean-field game with a major player; portfolio liquidation;
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