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Mean-Field Game Strategies for Optimal Execution

Author

Listed:
  • Xuancheng Huang
  • Sebastian Jaimungal
  • Mojtaba Nourian

Abstract

Algorithmic trading strategies for execution often focus on the individual agent who is liquidating/acquiring shares. When generalized to multiple agents, the resulting stochastic game is notoriously difficult to solve in closed-form. Here, we circumvent the difficulties by investigating a mean-field game framework containing (i) a major agent who is liquidating a large number of shares, (ii) a number of minor agents (high-frequency traders (HFTs)) who detect and trade against the liquidator, and (iii) noise traders who buy and sell for exogenous reasons. Our setup accounts for permanent price impact stemming from all trader types inducing an interaction between major and minor agents. Both optimizing agents trade against noise traders as well as one another. This stochastic dynamic game contains couplings in the price and trade dynamics, and we use a mean-field game approach to solve the problem. We obtain a set of decentralized feedback trading strategies for the major and minor agents, and express the solution explicitly in terms of a deterministic fixed point problem. For a finite $$N$$N population of HFTs, the set of major-minor agent mean-field game strategies is shown to have a $${{\epsilon}_N}$$ϵN -Nash equilibrium property where $${{\epsilon}_N} \to 0$$ϵN→0 as $$N \to \infty $$N→∞ .

Suggested Citation

  • Xuancheng Huang & Sebastian Jaimungal & Mojtaba Nourian, 2019. "Mean-Field Game Strategies for Optimal Execution," Applied Mathematical Finance, Taylor & Francis Journals, vol. 26(2), pages 153-185, March.
  • Handle: RePEc:taf:apmtfi:v:26:y:2019:i:2:p:153-185
    DOI: 10.1080/1350486X.2019.1603183
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    Citations

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    Cited by:

    1. David Evangelista & Yuri Thamsten, 2020. "On finite population games of optimal trading," Papers 2004.00790, arXiv.org, revised Feb 2021.
    2. Horst, Ulrich & Xia, Xiaonyu & Zhou, Chao, 2021. "Portfolio Liquidation under Factor Uncertainty," Rationality and Competition Discussion Paper Series 274, CRC TRR 190 Rationality and Competition.
    3. Eyal Neuman & Moritz Vo{ss}, 2021. "Trading with the Crowd," Papers 2106.09267, arXiv.org, revised Mar 2023.
    4. Arvind Shrivats & Dena Firoozi & Sebastian Jaimungal, 2020. "A Mean-Field Game Approach to Equilibrium Pricing in Solar Renewable Energy Certificate Markets," Papers 2003.04938, arXiv.org, revised Aug 2021.
    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. Moritz Vo{ss}, 2019. "A two-player portfolio tracking game," Papers 1911.05122, arXiv.org, revised Jul 2022.
    7. Fu, Guanxing & Horst, Ulrich & Xia, Xiaonyu, 2022. "Portfolio Liquidation Games with Self-Exciting Order Flow," Rationality and Competition Discussion Paper Series 327, CRC TRR 190 Rationality and Competition.
    8. Dena Firoozi & Arvind V Shrivats & Sebastian Jaimungal, 2021. "Principal agent mean field games in REC markets," Papers 2112.11963, arXiv.org, revised Jun 2022.
    9. Philippe Bergault & Leandro S'anchez-Betancourt, 2024. "A Mean Field Game between Informed Traders and a Broker," Papers 2401.05257, arXiv.org.
    10. Xue Cheng & Meng Wang & Ziyi Xu, 2024. "Mean Field Game of High-Frequency Anticipatory Trading," Papers 2404.18200, arXiv.org.
    11. Sebastian Jaimungal, 2022. "Reinforcement learning and stochastic optimisation," Finance and Stochastics, Springer, vol. 26(1), pages 103-129, January.
    12. Yufan Chen & Lan Wu & Renyuan Xu & Ruixun Zhang, 2024. "Periodic Trading Activities in Financial Markets: Mean-field Liquidation Game with Major-Minor Players," Papers 2408.09505, arXiv.org.
    13. Bastien Baldacci & Philippe Bergault & Dylan Possamai, 2022. "A mean-field game of market-making against strategic traders," Papers 2203.13053, arXiv.org.
    14. Guanxing Fu & Ulrich Horst & Xiaonyu Xia, 2020. "Portfolio Liquidation Games with Self-Exciting Order Flow," Papers 2011.05589, arXiv.org.
    15. Paulwin Graewe & Ulrich Horst & Ronnie Sircar, 2021. "A Maximum Principle approach to deterministic Mean Field Games of Control with Absorption," Papers 2104.06152, arXiv.org.
    16. Ludovic Tangpi & Shichun Wang, 2022. "Optimal Bubble Riding: A Mean Field Game with Varying Entry Times," Papers 2209.04001, arXiv.org, revised Jan 2024.
    17. Ulrich Horst & Xiaonyu Xia & Chao Zhou, 2019. "Portfolio liquidation under factor uncertainty," Papers 1909.00748, arXiv.org.
    18. Masamitsu Ohnishi & Makoto Shimoshimizu, 2024. "Trade execution games in a Markovian environment," Papers 2405.07184, arXiv.org.
    19. Guillermo Alonso Alvarez & Sergey Nadtochiy & Kevin Webster, 2022. "Optimal brokerage contracts in Almgren-Chriss model with multiple clients," Papers 2204.05403, arXiv.org.
    20. Steven Campbell & Yichao Chen & Arvind Shrivats & Sebastian Jaimungal, 2021. "Deep Learning for Principal-Agent Mean Field Games," Papers 2110.01127, arXiv.org.
    21. Hanchao Liu & Dena Firoozi & Mich`ele Breton, 2023. "LQG Risk-Sensitive Single-Agent and Major-Minor Mean Field Game Systems: A Variational Framework," Papers 2305.15364, arXiv.org, revised Aug 2023.
    22. Moritz Voß, 2022. "A two-player portfolio tracking game," Mathematics and Financial Economics, Springer, volume 16, number 6, March.

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