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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
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    References listed on IDEAS

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    1. 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.
    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. 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.
    4. William M. Boyce, 1970. "Stopping Rules for Selling Bonds," Bell Journal of Economics, The RAND Corporation, vol. 1(1), pages 27-53, Spring.
    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. Albert Shiryaev & Zuoquan Xu & Xun Yu Zhou, 2008. "Thou shalt buy and hold," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 765-776.
    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.
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    Cited by:

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    8. 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).
    9. Zhenya Liu & Yuhao Mu, 2022. "Optimal Stopping Methods for Investment Decisions: A Literature Review," IJFS, MDPI, vol. 10(4), pages 1-23, October.
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