IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v151y2011i2d10.1007_s10957-011-9897-0.html
   My bibliography  Save this article

Optimal Decision for Selling an Illiquid Stock

Author

Listed:
  • Baojun Bian

    (Tongji University)

  • Min Dai

    (National University of Singapore (NUS))

  • Lishang Jiang

    (Tongji University)

  • Qing Zhang

    (The University of Georgia)

  • Yifei Zhong

    (Oxford University)

Abstract

This paper is concerned with liquidation of an illiquid stock. The stock price follows a fluid model which is dictated by the rates of selling and buying over time. The objective is to maximize the expected overall return. The method of constrained viscosity solution is used to characterize the dynamics governing the optimal reward function and the associated boundary conditions. Numerical examples are given to illustrate the results.

Suggested Citation

  • Baojun Bian & Min Dai & Lishang Jiang & Qing Zhang & Yifei Zhong, 2011. "Optimal Decision for Selling an Illiquid Stock," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 402-417, November.
    • Handle: RePEc:spr:joptap:v:151:y:2011:i:2:d:10.1007_s10957-011-9897-0
    DOI: 10.1007/s10957-011-9897-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-011-9897-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-011-9897-0?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. Dai, Min & Kwok, Yue Kuen & You, Hong, 2007. "Intensity-based framework and penalty formulation of optimal stopping problems," Journal of Economic Dynamics and Control, Elsevier, vol. 31(12), pages 3860-3880, December.
    2. 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.
    3. Longstaff, Francis A, 2001. "Optimal Portfolio Choice and the Valuation of Illiquid Securities," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 407-431.
    4. Pemy, M. & Zhang, Q. & Yin, G., 2007. "Liquidation of a large block of stock," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1295-1305, May.
    5. Ajay Subramanian & Robert A. Jarrow, 2001. "The Liquidity Discount," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 447-474, October.
    6. 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.
    7. Min Dai & Yue Kuen Kwok & Jianping Zong, 2008. "Guaranteed Minimum Withdrawal Benefit In Variable Annuities," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 595-611, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hidekazu Yoshioka & Yuta Yaegashi, 2020. "A growth rate control problem of harmful species population and its application to algae bloom," Environment Systems and Decisions, Springer, vol. 40(1), pages 107-124, March.

    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. Mauricio Junca, 2011. "Stochastic impulse control on optimal execution with price impact and transaction cost," Papers 1103.3482, arXiv.org, revised Jan 2013.
    2. Olivier Guéant & Charles-Albert Lehalle, 2015. "General Intensity Shapes In Optimal Liquidation," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 457-495, July.
    3. Samuel N. Cohen & Lukasz Szpruch, 2011. "A limit order book model for latency arbitrage," Papers 1110.4811, arXiv.org.
    4. 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.
    5. Aurélien Alfonsi & Alexander Schied, 2010. "Optimal trade execution and absence of price manipulations in limit order book models," Post-Print hal-00397652, HAL.
    6. Masashi Ieda, 2015. "A dynamic optimal execution strategy under stochastic price recovery," Papers 1502.04521, arXiv.org.
    7. Olivier Gu'eant, 2013. "Permanent market impact can be nonlinear," Papers 1305.0413, arXiv.org, revised Mar 2014.
    8. Sergey Isaenko & Rui Zhong, 2015. "Liquidity premium in the presence of stock market crises and background risk," Quantitative Finance, Taylor & Francis Journals, vol. 15(1), pages 79-90, January.
    9. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    10. Erhan Bayraktar & Thomas Cayé & Ibrahim Ekren, 2021. "Asymptotics for small nonlinear price impact: A PDE approach to the multidimensional case," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 36-108, January.
    11. Vayanos, Dimitri & Wang, Jiang, 2013. "Market Liquidity—Theory and Empirical Evidence ," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1289-1361, Elsevier.
    12. He, Hua & Mamaysky, Harry, 2005. "Dynamic trading policies with price impact," Journal of Economic Dynamics and Control, Elsevier, vol. 29(5), pages 891-930, May.
    13. Peter Bank & Mete Soner & Moritz Vo{ss}, 2015. "Hedging with Temporary Price Impact," Papers 1510.03223, arXiv.org, revised Jul 2016.
    14. Masashi Ieda, 2015. "A dynamic optimal execution strategy under stochastic price recovery," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 1-24, December.
    15. Peter Bank & Dmitry Kramkov, 2015. "A model for a large investor trading at market indifference prices. I: Single-period case," Finance and Stochastics, Springer, vol. 19(2), pages 449-472, April.
    16. Somayeh Moazeni & Thomas Coleman & Yuying Li, 2013. "Regularized robust optimization: the optimal portfolio execution case," Computational Optimization and Applications, Springer, vol. 55(2), pages 341-377, June.
    17. Brunovský, Pavol & Černý, Aleš & Komadel, Ján, 2018. "Optimal trade execution under endogenous pressure to liquidate: Theory and numerical solutions," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1159-1171.
    18. Nikolay A. Andreev, 2015. "Worst-Case Approach To Strategic Optimal Portfolio Selection Under Transaction Costs And Trading Limits," HSE Working papers WP BRP 45/FE/2015, National Research University Higher School of Economics.
    19. Xiao Chen & Jin Hyuk Choi & Kasper Larsen & Duane J. Seppi, 2021. "Learning about latent dynamic trading demand," Papers 2105.13401, arXiv.org, revised Aug 2021.
    20. Peter Kratz & Torsten Schoneborn, 2012. "Portfolio liquidation in dark pools in continuous time," Papers 1201.6130, arXiv.org, revised Aug 2012.

    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:spr:joptap:v:151:y:2011:i:2:d:10.1007_s10957-011-9897-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.