IDEAS home Printed from https://ideas.repec.org/a/eee/finlet/v61y2024ics1544612324000734.html
   My bibliography  Save this article

Viscosity solution for optimal liquidation problems with randomly-terminated horizon

Author

Listed:
  • Yang, Qing-Qing
  • Ching, Wai-Ki
  • Gu, Jia-wen
  • Wong, Tak Kwong
  • Zhu, Dong-Mei

Abstract

In this paper, we study an optimal liquidation problem of a stressed asset, for which its value is modeled by a geometric Brownian motion. The default time of the stressed asset, therefore, becomes stochastic and predictable. Hence we deal with the optimal liquidation problem in a randomly-terminated horizon. We consider the liquidation of a large single-asset portfolio with the aim of minimizing a combination of volatility risk and transaction costs arising from permanent and temporary market impacts. We prove that the value function is the unique viscosity solution to the Hamilton–Jacobi–Bellman (HJB) equation of the considered optimal liquidation problem.

Suggested Citation

  • Yang, Qing-Qing & Ching, Wai-Ki & Gu, Jia-wen & Wong, Tak Kwong & Zhu, Dong-Mei, 2024. "Viscosity solution for optimal liquidation problems with randomly-terminated horizon," Finance Research Letters, Elsevier, vol. 61(C).
    • Handle: RePEc:eee:finlet:v:61:y:2024:i:c:s1544612324000734
    DOI: 10.1016/j.frl.2024.105043
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1544612324000734
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.frl.2024.105043?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Alexander Schied & Torsten Schöneborn, 2009. "Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets," Finance and Stochastics, Springer, vol. 13(2), pages 181-204, April.
    2. Sadoghi, Amirhossein & Vecer, Jan, 2022. "Optimal liquidation problem in illiquid markets," European Journal of Operational Research, Elsevier, vol. 296(3), pages 1050-1066.
    3. Alexandre Roch, 2023. "Optimal Liquidation Through a Limit Order Book: A Neural Network and Simulation Approach," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-29, March.
    4. Francesca Mariani & Lorella Fatone, 2022. "Optimal solution of the liquidation problem under execution and price impact risks," Quantitative Finance, Taylor & Francis Journals, vol. 22(6), pages 1037-1049, June.
    5. Xue Cheng & Marina Di Giacinto & Tai-Ho Wang, 2019. "Optimal execution with dynamic risk adjustment," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(10), pages 1662-1677, October.
    6. 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.
    7. 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.
    8. Xue Cheng & Marina Di Giacinto & Tai-Ho Wang, 2019. "Optimal execution with dynamic risk adjustment," Papers 1901.00617, arXiv.org, revised Jul 2019.
    9. Robert Almgren, 2003. "Optimal execution with nonlinear impact functions and trading-enhanced risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 1-18.
    10. Amirhossein Sadoghi & Jan Vecer, 2022. "Optimal liquidation problem in illiquid markets," Post-Print hal-03696768, HAL.
    11. 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.
    12. Shahin Abbaszadeh & Tri-Dung Nguyen & Yue Wu, 2018. "Optimal trading under non-negativity constraints using approximate dynamic programming," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 69(9), pages 1406-1422, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Graewe, Paulwin & Popier, Alexandre, 2021. "Asymptotic approach for backward stochastic differential equation with singular terminal condition," Stochastic Processes and their Applications, Elsevier, vol. 133(C), pages 247-277.
    2. Julia Ackermann & Thomas Kruse & Mikhail Urusov, 2021. "Càdlàg semimartingale strategies for optimal trade execution in stochastic order book models," Finance and Stochastics, Springer, vol. 25(4), pages 757-810, October.
    3. Meng Wang & Tai-Ho Wang, 2023. "Relative entropy-regularized robust optimal order execution," Papers 2311.06476, arXiv.org, revised Sep 2024.
    4. Elliott, Robert & Qiu, Jinniao & Wei, Wenning, 2022. "Neumann problem for backward SPDEs with singular terminal conditions and application in constrained stochastic control under target zone," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 68-97.
    5. Alexandre Roch, 2023. "Optimal Liquidation Through a Limit Order Book: A Neural Network and Simulation Approach," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-29, March.
    6. Max O. Souza & Yuri Thamsten, 2021. "On regularized optimal execution problems and their singular limits," Papers 2101.02731, arXiv.org, revised Aug 2023.
    7. Dupret, Jean-Loup & Hainaut, Donatien, 2023. "Optimal liquidation under indirect price impact with propagator," LIDAM Discussion Papers ISBA 2023012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. 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.
    9. Ulrich Horst & Xiaonyu Xia, 2018. "Continuous viscosity solutions to linear-quadratic stochastic control problems with singular terminal state constraint," Papers 1809.01972, arXiv.org, revised Apr 2020.
    10. Ulrich Horst & Xiaonyu Xia & Chao Zhou, 2019. "Portfolio liquidation under factor uncertainty," Papers 1909.00748, arXiv.org.
    11. Daniel Hern'andez-Hern'andez & Harold A. Moreno-Franco & Jos'e Luis P'erez, 2017. "Periodic strategies in optimal execution with multiplicative price impact," Papers 1705.00284, arXiv.org, revised May 2018.
    12. Olivier Guéant & Charles-Albert Lehalle, 2015. "General Intensity Shapes In Optimal Liquidation," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 457-495, July.
    13. Marina Di Giacinto & Claudio Tebaldi & Tai-Ho Wang, 2021. "Optimal order execution under price impact: A hybrid model," Papers 2112.02228, arXiv.org, revised Aug 2022.
    14. Tim Leung & Yoshihiro Shirai, 2015. "Optimal derivative liquidation timing under path-dependent risk penalties," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(01), pages 1-32.
    15. Aurélien Alfonsi & Alexander Schied, 2010. "Optimal trade execution and absence of price manipulations in limit order book models," Post-Print hal-00397652, HAL.
    16. Masashi Ieda, 2015. "A dynamic optimal execution strategy under stochastic price recovery," Papers 1502.04521, arXiv.org.
    17. Xiao Chen & Jin Hyuk Choi & Kasper Larsen & Duane J. Seppi, 2019. "Resolving asset pricing puzzles using price-impact," Papers 1910.02466, arXiv.org, revised Jun 2020.
    18. Guanxing Fu & Ulrich Horst, 2018. "Mean-Field Leader-Follower Games with Terminal State Constraint," Papers 1809.04401, arXiv.org.
    19. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    20. Olivier Gu'eant, 2013. "Permanent market impact can be nonlinear," Papers 1305.0413, arXiv.org, revised Mar 2014.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:finlet:v:61:y:2024:i:c:s1544612324000734. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/frl .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.