IDEAS home Printed from https://ideas.repec.org/a/inm/ormoor/v45y2020i1p384-401.html
   My bibliography  Save this article

Optimal Redeeming Strategy of Stock Loans Under Drift Uncertainty

Author

Listed:
  • Zuo Quan Xu

    (Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;)

  • Fahuai Yi

    (School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou, 510006 Guangdong, China)

Abstract

In practice, one must recognize the inevitable incompleteness of information while making decisions. In this paper, we consider the optimal redeeming problem of stock loans under a state of incomplete information presented by the uncertainty in the (bull or bear) trends of the underlying stock. This is called drift uncertainty. Owing to the unavoidable need for the estimation of trends while making decisions, the related Hamilton–Jacobi–Bellman equation turns out to be of a degenerate parabolic type. Hence, it is very hard to obtain its regularity using the standard approach, making the problem different from the existing optimal redeeming problems without drift uncertainty. We present a thorough and delicate probabilistic and functional analysis to obtain the regularity of the value function and the optimal redeeming strategies. The optimal redeeming strategies of stock loans appear significantly different in the bull and bear trends.

Suggested Citation

  • Zuo Quan Xu & Fahuai Yi, 2020. "Optimal Redeeming Strategy of Stock Loans Under Drift Uncertainty," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 384-401, February.
    • Handle: RePEc:inm:ormoor:v:45:y:2020:i:1:p:384-401
    DOI: 10.1287/moor.2019.0995
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/moor.2019.0995
    Download Restriction: no
    File URL: https://libkey.io/10.1287/moor.2019.0995?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
    ---><---

    References listed on IDEAS

    as
    1. Zuo Quan Xu, 2016. "A Note On The Quantile Formulation," Mathematical Finance, Wiley Blackwell, vol. 26(3), pages 589-601, July.
    2. Albert Shiryaev & Zuoquan Xu & Xun Yu Zhou, 2008. "Response to comment on 'Thou shalt buy and hold'," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 761-762.
    3. Tim Leung & Xin Li & Zheng Wang, 2015. "Optimal Multiple Trading Times Under the Exponential OU Model with Transaction Costs," Papers 1504.04682, arXiv.org.
    4. Jean-Paul Décamps & Thomas Mariotti & Stéphane Villeneuve, 2005. "Investment Timing Under Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 472-500, May.
    5. Jérôme Detemple & Weidong Tian & Jie Xiong, 2012. "An optimal stopping problem with a reward constraint," Finance and Stochastics, Springer, vol. 16(3), pages 423-448, July.
    6. Xun Li & Hwee Huat Tan & Craig Wilson & Zhenyu Wu, 2013. "When should venture capitalists exit their investee companies?," International Journal of Managerial Finance, Emerald Group Publishing Limited, vol. 9(4), pages 351-364, September.
    7. Zuo Quan Xu & Xun Yu Zhou, 2011. "Optimal stopping under probability distortion," Papers 1103.1755, arXiv.org, revised Feb 2013.
    8. Albert Shiryaev & Zuoquan Xu & Xun Yu Zhou, 2008. "Thou shalt buy and hold," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 765-776.
    9. X. Guo, 2001. "Information and option pricings," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 38-44.
    10. Erik Ekstrom & Juozas Vaicenavicius, 2015. "Optimal liquidation of an asset under drift uncertainty," Papers 1509.00686, arXiv.org.
    11. Xiong, Jie, 2008. "An Introduction to Stochastic Filtering Theory," OUP Catalogue, Oxford University Press, number 9780199219704.
    12. Cai, Ning & Sun, Lihua, 2014. "Valuation of stock loans with jump risk," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 213-241.
    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. Xing, Jie & Ma, Jingtang & Yang, Wensheng, 2023. "Optimal entry decision of unemployment insurance under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 31-52.

    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. Zuo Quan Xu & Fahuai Yi, 2019. "Optimal redeeming strategy of stock loans under drift uncertainty," Papers 1901.06680, arXiv.org.
    2. Tim Leung & Xin Li & Zheng Wang, 2014. "Optimal Starting-Stopping and Switching of a CIR Process with Fixed Costs," Papers 1411.6080, arXiv.org.
    3. Sabri Boubaker & Zhenya Liu & Yaosong Zhan, 2022. "Risk management for crude oil futures: an optimal stopping-timing approach," Annals of Operations Research, Springer, vol. 313(1), pages 9-27, June.
    4. Nader Karimi & Hirbod Assa & Erfan Salavati & Hojatollah Adibi, 2023. "Calibration of Storage Model by Multi-Stage Statistical and Machine Learning Methods," Computational Economics, Springer;Society for Computational Economics, vol. 62(4), pages 1437-1455, December.
    5. Alex S. L. Tse & Harry Zheng, 2023. "Speculative trading, prospect theory and transaction costs," Finance and Stochastics, Springer, vol. 27(1), pages 49-96, January.
    6. Satya Majumdar & Jean-Philippe Bouchaud, 2008. "Optimal time to sell a stock in the Black-Scholes model: comment on 'Thou shalt buy and hold', by A. Shiryaev, Z. Xu and X.Y. Zhou," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 753-760.
    7. Arcand, Jean-Louis & Hongler, Max-Olivier & Rinaldo, Daniele, 2020. "Increasing risk: Dynamic mean-preserving spreads," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 69-82.
    8. L. Rüschendorf & Steven Vanduffel, 2020. "On the construction of optimal payoffs," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 129-153, June.
    9. Yue Liu & Aijun Yang & Jijian Zhang & Jingjing Yao, 2020. "An Optimal Stopping Problem of Detecting Entry Points for Trading Modeled by Geometric Brownian Motion," Computational Economics, Springer;Society for Computational Economics, vol. 55(3), pages 827-843, March.
    10. Tim Leung & Xin Li & Zheng Wang, 2015. "Optimal Multiple Trading Times Under the Exponential OU Model with Transaction Costs," Papers 1504.04682, arXiv.org.
    11. Min Dai & Zhou Yang & Qing Zhang & Qiji Jim Zhu, 2016. "Optimal Trend Following Trading Rules," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 626-642, May.
    12. Jordan Mann & J. Nathan Kutz, 2016. "Dynamic mode decomposition for financial trading strategies," Quantitative Finance, Taylor & Francis Journals, vol. 16(11), pages 1643-1655, November.
    13. Mingyu Xu & Zuo Quan Xu & Xun Yu Zhou, 2022. "$g$-Expectation of Distributions," Papers 2208.06535, arXiv.org.
    14. Xiongfei Jian & Xun Li & Fahuai Yi, 2014. "Optimal Investment with Stopping in Finite Horizon," Papers 1406.6940, arXiv.org.
    15. Christoph Kuhn & Budhi Arta Surya & Bjorn Ulbricht, 2014. "Optimal Selling Time of a Stock under Capital Gains Taxes," Papers 1501.00026, arXiv.org.
    16. Eddie C. M. Hui & Ka Kwan Kevin Chan, 2018. "Testing Calendar Effects of International Equity and Real Estate Markets," The Journal of Real Estate Finance and Economics, Springer, vol. 56(1), pages 140-158, January.
    17. Ameur, Hachmi Ben & Han, Xuyuan & Liu, Zhenya & Peillex, Jonathan, 2022. "When did global warming start? A new baseline for carbon budgeting," Economic Modelling, Elsevier, vol. 116(C).
    18. Zhenya Liu & Yuhao Mu, 2022. "Optimal Stopping Methods for Investment Decisions: A Literature Review," IJFS, MDPI, vol. 10(4), pages 1-23, October.
    19. Souradeep Chakraborty, 2019. "Capturing Financial markets to apply Deep Reinforcement Learning," Papers 1907.04373, arXiv.org, revised Dec 2019.
    20. Denis Belomestny & Volker Krätschmer, 2017. "Optimal Stopping Under Probability Distortions," Mathematics of Operations Research, INFORMS, vol. 42(3), pages 806-833, August.

    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:inm:ormoor:v:45:y:2020:i:1:p:384-401. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.