IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1601.00175.html
   My bibliography  Save this paper

Minimax perfect stopping rules for selling an asset near its ultimate maximum

Author

Listed:
  • Dmitry B. Rokhlin

Abstract

We study the problem of selling an asset near its ultimate maximum in the minimax setting. The regret-based notion of a perfect stopping time is introduced. A perfect stopping time is uniquely characterized by its optimality properties and has the following form: one should sell the asset if its price deviates from the running maximum by a certain time-dependent quantity. The related selling rule improves any earlier one and cannot be improved by further delay. The results, which are applicable to a quite general price model, are illustrated by several examples.

Suggested Citation

  • Dmitry B. Rokhlin, 2016. "Minimax perfect stopping rules for selling an asset near its ultimate maximum," Papers 1601.00175, arXiv.org, revised Jul 2016.
    • Handle: RePEc:arx:papers:1601.00175
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1601.00175
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Gordon Pye, 1971. "Minimax Policies for Selling an Asset and Dollar Averaging," Management Science, INFORMS, vol. 17(7), pages 379-393, March.
    3. Albert Shiryaev & Zuoquan Xu & Xun Yu Zhou, 2008. "Thou shalt buy and hold," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 765-776.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Tim Leung & Xin Li & Zheng Wang, 2015. "Optimal Multiple Trading Times Under the Exponential OU Model with Transaction Costs," Papers 1504.04682, arXiv.org.
    7. 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.
    8. 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.
    9. Zuo Quan Xu & Fahuai Yi, 2019. "Optimal redeeming strategy of stock loans under drift uncertainty," Papers 1901.06680, arXiv.org.
    10. Xiongfei Jian & Xun Li & Fahuai Yi, 2014. "Optimal Investment with Stopping in Finite Horizon," Papers 1406.6940, arXiv.org.
    11. Christoph Kuhn & Budhi Arta Surya & Bjorn Ulbricht, 2014. "Optimal Selling Time of a Stock under Capital Gains Taxes," Papers 1501.00026, arXiv.org.
    12. Tim Leung & Xin Li & Zheng Wang, 2014. "Optimal Starting-Stopping and Switching of a CIR Process with Fixed Costs," Papers 1411.6080, arXiv.org.
    13. 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.
    14. 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).
    15. Zhenya Liu & Yuhao Mu, 2022. "Optimal Stopping Methods for Investment Decisions: A Literature Review," IJFS, MDPI, vol. 10(4), pages 1-23, October.
    16. Souradeep Chakraborty, 2019. "Capturing Financial markets to apply Deep Reinforcement Learning," Papers 1907.04373, arXiv.org, revised Dec 2019.
    17. Xun Li & Xianping Wu & Wenxin Zhou, 2017. "Optimal stopping investment in a logarithmic utility-based portfolio selection problem," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 3(1), pages 1-10, December.
    18. Yue Liu & Nicolas Privault, 2017. "Selling At The Ultimate Maximum In A Regime-Switching Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-27, May.
    19. Hui, Eddie C.M. & Chan, Ka Kwan Kevin, 2019. "Alternative trading strategies to beat “buy-and-hold”," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    20. 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.

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:1601.00175. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.