IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v55y2020i3d10.1007_s10614-019-09915-w.html
   My bibliography  Save this article

An Optimal Stopping Problem of Detecting Entry Points for Trading Modeled by Geometric Brownian Motion

Author

Listed:
  • Yue Liu

    (Jiangsu University)

  • Aijun Yang

    (Nanjing Forestry University)

  • Jijian Zhang

    (Jiangsu University)

  • Jingjing Yao

    (Jiangsu University)

Abstract

A “buy low, sell high” trading practice is modeled as an optimal stopping problem in this paper. Because its award function lacks sufficient smoothness, traditional free-boundary approach with solution in form of integral equations is not available. Therefore, we design a backward recursive algorithm computing the value function to determine the stopping boundary. Besides, a new PDE technique is developed to conclude the special cases with positive drift. Finally, groups of comparison tests are designed to investigate the model parameters setting as well as the feasibility and profitability of the trading strategy.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:compec:v:55:y:2020:i:3:d:10.1007_s10614-019-09915-w
    DOI: 10.1007/s10614-019-09915-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10614-019-09915-w
    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/s10614-019-09915-w?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. William M. Boyce, 1970. "Stopping Rules for Selling Bonds," Bell Journal of Economics, The RAND Corporation, vol. 1(1), pages 27-53, Spring.
    2. David D. Yao & Qing Zhang & Xun Yu Zhou, 2006. "A Regime-Switching Model for European Options," International Series in Operations Research & Management Science, in: Houmin Yan & George Yin & Qing Zhang (ed.), Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems, chapter 0, pages 281-300, Springer.
    3. 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.
    4. Albert Shiryaev & Zuoquan Xu & Xun Yu Zhou, 2008. "Thou shalt buy and hold," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 765-776.
    5. Yang, Aijun & Liu, Yue & Xiang, Ju & Yang, Hongqiang, 2016. "Optimal buying at the global minimum in a regime switching model," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 50-55.
    6. Yue Liu & Nicolas Privault, 2018. "A Recursive Algorithm for Selling at the Ultimate Maximum in Regime-Switching Models," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 369-384, March.
    7. 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.
    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. Yue Liu & Jijian Zhang & Xuhui Ding & Xiling Zhang, 2023. "Intervene in advance or passively? Analysis and application on congestion control of smart grid," Annals of Operations Research, Springer, vol. 320(2), pages 887-899, January.
    2. Zhenya Liu & Yuhao Mu, 2022. "Optimal Stopping Methods for Investment Decisions: A Literature Review," IJFS, MDPI, vol. 10(4), pages 1-23, October.
    3. Gil Cohen, 2022. "Artificial Intelligence in Trading the Financial Markets," International Journal of Economics & Business Administration (IJEBA), International Journal of Economics & Business Administration (IJEBA), vol. 0(1), pages 101-110.
    4. Peixin Duan, 2022. "How large of a grant size is appropriate? Evidence from the National Natural Science Foundation of China," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-14, February.
    5. Gil Cohen, 2021. "Optimizing candlesticks patterns for Bitcoin's trading systems," Review of Quantitative Finance and Accounting, Springer, vol. 57(3), pages 1155-1167, October.
    6. Liu, Yue & Tian, Lixin & Sun, Huaping & Zhang, Xiling & Kong, Chuimin, 2022. "Option pricing of carbon asset and its application in digital decision-making of carbon asset," Applied Energy, Elsevier, vol. 310(C).
    7. Yue Liu & Lixin Tian & Zhuyun Xie & Zaili Zhen & Huaping Sun, 2021. "Option to survive or surrender: carbon asset management and optimization in thermal power enterprises from China," Papers 2104.04729, arXiv.org.
    8. Gil Cohen, 2021. "Trading Cryptocurrencies Using Second Order Stochastic Dominance," Mathematics, MDPI, vol. 9(22), pages 1-10, November.
    9. Gil Cohen, 2021. "Optimizing Algorithmic Strategies for Trading Bitcoin," Computational Economics, Springer;Society for Computational Economics, vol. 57(2), pages 639-654, February.
    10. Liu, Yue & Sun, Huaping & Meng, Bo & Jin, Shunlin & Chen, Bin, 2023. "How to purchase carbon emission right optimally for energy-consuming enterprises? Analysis based on optimal stopping model," Energy Economics, Elsevier, vol. 124(C).
    11. Gil Cohen, 2023. "Intraday algorithmic trading strategies for cryptocurrencies," Review of Quantitative Finance and Accounting, Springer, vol. 61(1), pages 395-409, July.

    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. 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.
    2. Liu, Yue & Sun, Huaping & Zhang, Jijian & Taghizadeh-Hesary, Farhad, 2020. "Detection of volatility regime-switching for crude oil price modeling and forecasting," Resources Policy, Elsevier, vol. 69(C).
    3. 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.
    4. 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.
    5. Xiongfei Jian & Xun Li & Fahuai Yi, 2014. "Optimal Investment with Stopping in Finite Horizon," Papers 1406.6940, arXiv.org.
    6. Christoph Kuhn & Budhi Arta Surya & Bjorn Ulbricht, 2014. "Optimal Selling Time of a Stock under Capital Gains Taxes," Papers 1501.00026, arXiv.org.
    7. Yue Liu & Nicolas Privault, 2018. "A Recursive Algorithm for Selling at the Ultimate Maximum in Regime-Switching Models," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 369-384, March.
    8. 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).
    9. Zhenya Liu & Yuhao Mu, 2022. "Optimal Stopping Methods for Investment Decisions: A Literature Review," IJFS, MDPI, vol. 10(4), pages 1-23, October.
    10. 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.
    11. 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).
    12. Dmitry B. Rokhlin, 2016. "Minimax perfect stopping rules for selling an asset near its ultimate maximum," Papers 1601.00175, arXiv.org, revised Jul 2016.
    13. 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.
    14. 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.
    15. 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.
    16. Tim Leung & Xin Li & Zheng Wang, 2015. "Optimal Multiple Trading Times Under the Exponential OU Model with Transaction Costs," Papers 1504.04682, arXiv.org.
    17. 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.
    18. Zuo Quan Xu & Fahuai Yi, 2019. "Optimal redeeming strategy of stock loans under drift uncertainty," Papers 1901.06680, arXiv.org.
    19. Yang, Aijun & Liu, Yue & Xiang, Ju & Yang, Hongqiang, 2016. "Optimal buying at the global minimum in a regime switching model," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 50-55.
    20. Tim Leung & Xin Li & Zheng Wang, 2014. "Optimal Starting-Stopping and Switching of a CIR Process with Fixed Costs," Papers 1411.6080, arXiv.org.

    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:kap:compec:v:55:y:2020:i:3:d:10.1007_s10614-019-09915-w. 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.