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Deep learning solution to mean field game of optimal liquidation

Author

Listed:
  • Zhang, Shuhua
  • Qian, Shenghua
  • Wang, Xinyu
  • Cheng, Yilin

Abstract

This paper addresses optimal portfolio liquidation using Mean Field Games (MFGs) and presents a solution method to tackle high-dimensional challenges. We develop a deep learning approach that employs two sub-networks to approximate solutions to the relevant partial differential equations. Our method adheres to the requirements of differential operators and satisfies both initial and terminal conditions through simultaneous training. A key advantage of our approach is its mesh-free nature, which mitigates the curse of dimensionality encountered in traditional numerical methods. We validate the effectiveness of our approach through numerical experiments on multi-dimensional portfolio liquidation models.

Suggested Citation

  • Zhang, Shuhua & Qian, Shenghua & Wang, Xinyu & Cheng, Yilin, 2025. "Deep learning solution to mean field game of optimal liquidation," Finance Research Letters, Elsevier, vol. 73(C).
    • Handle: RePEc:eee:finlet:v:73:y:2025:i:c:s1544612324016921
    DOI: 10.1016/j.frl.2024.106663
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    References listed on IDEAS

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    1. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Finance and Stochastics, Springer, vol. 20(1), pages 183-218, January.
    2. 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.
    3. 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.
    4. Aur'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756, arXiv.org, revised Feb 2010.
    5. Aurelien Alfonsi & Antje Fruth & Alexander Schied, 2010. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 143-157.
    6. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Finance and Stochastics, Springer, vol. 20(1), pages 183-218, January.
    7. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    8. Ali Al-Aradi & Adolfo Correia & Danilo Naiff & Gabriel Jardim & Yuri Saporito, 2018. "Solving Nonlinear and High-Dimensional Partial Differential Equations via Deep Learning," Papers 1811.08782, arXiv.org.
    9. Guanxing Fu & Paulwin Graewe & Ulrich Horst & Alexandre Popier, 2021. "A Mean Field Game of Optimal Portfolio Liquidation," Mathematics of Operations Research, INFORMS, vol. 46(4), pages 1250-1281, November.
    10. Paulwin Graewe & Ulrich Horst & Eric S'er'e, 2013. "Smooth solutions to portfolio liquidation problems under price-sensitive market impact," Papers 1309.0474, arXiv.org, revised Jun 2017.
    11. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Post-Print hal-00971369, HAL.
    12. Justin Sirignano & Konstantinos Spiliopoulos, 2017. "DGM: A deep learning algorithm for solving partial differential equations," Papers 1708.07469, arXiv.org, revised Sep 2018.
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