IDEAS home Printed from https://ideas.repec.org/a/spr/fininn/v3y2017i1d10.1186_s40854-017-0080-y.html
   My bibliography  Save this article

Optimal stopping investment in a logarithmic utility-based portfolio selection problem

Author

Listed:
  • Xun Li

    (The Hong Kong Polytechnic University)

  • Xianping Wu

    (South China Normal University)

  • Wenxin Zhou

    (The Hong Kong Polytechnic University)

Abstract

Background In this paper, we study the right time for an investor to stop the investment over a given investment horizon so as to obtain as close to the highest possible wealth as possible, according to a Logarithmic utility-maximization objective involving the portfolio in the drift and volatility terms. The problem is formulated as an optimal stopping problem, although it is non-standard in the sense that the maximum wealth involved is not adapted to the information generated over time. Methods By delicate stochastic analysis, the problem is converted to a standard optimal stopping one involving adapted processes. Results Numerical examples shed light on the efficiency of the theoretical results. Conclusion Our investment problem, which includes the portfolio in the drift and volatility terms of the dynamic systems, makes the problem including multi-dimensional financial assets more realistic and meaningful.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:fininn:v:3:y:2017:i:1:d:10.1186_s40854-017-0080-y
    DOI: 10.1186/s40854-017-0080-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1186/s40854-017-0080-y
    File Function: Abstract
    Download Restriction: no
    File URL: https://libkey.io/10.1186/s40854-017-0080-y?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. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    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. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    5. Dayanik, Savas & Karatzas, Ioannis, 2003. "On the optimal stopping problem for one-dimensional diffusions," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 173-212, October.
    6. Kyoung Jin Choi & Hyeng Keun Koo & Do Young Kwak, 2004. "Optimal Stopping of Active Portfolio Management," Annals of Economics and Finance, Society for AEF, vol. 5(1), pages 93-126, May.
    7. Albert Shiryaev & Zuoquan Xu & Xun Yu Zhou, 2008. "Thou shalt buy and hold," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 765-776.
    8. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    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. Masoud Rahiminezhad Galankashi & Farimah Mokhatab Rafiei & Maryam Ghezelbash, 2020. "Portfolio selection: a fuzzy-ANP approach," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-34, December.
    2. Yanzhao Li & Ju-e Guo & Shaolong Sun & Yongwu Li, 2022. "How time-inconsistent preferences influence venture capital exit decisions? A new perspective for grandstanding," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-24, December.

    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. Venegas-Martínez, Francisco & Polanco-Gaytán, Mayrén (ed.), 2011. "Macroeconomía Estocástica," Sección de Estudios de Posgrado e Investigación de la Escuela Superios de Economía del Instituto Politécnico Nacional, Escuela Superior de Economía, Instituto Politécnico Nacional, edition 1, volume 1, number 005, July.
    2. Xiongfei Jian & Xun Li & Fahuai Yi, 2014. "Optimal Investment with Stopping in Finite Horizon," Papers 1406.6940, arXiv.org.
    3. Zhenya Liu & Yuhao Mu, 2022. "Optimal Stopping Methods for Investment Decisions: A Literature Review," IJFS, MDPI, vol. 10(4), pages 1-23, October.
    4. Xikui Wang & Yanqing Yi, 2009. "An optimal investment and consumption model with stochastic returns," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(1), pages 45-55, January.
    5. 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).
    6. Munk, Claus, 2015. "Financial Asset Pricing Theory," OUP Catalogue, Oxford University Press, number 9780198716457.
    7. Hong‐Chih Huang, 2010. "Optimal Multiperiod Asset Allocation: Matching Assets to Liabilities in a Discrete Model," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(2), pages 451-472, June.
    8. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    9. Jan Kallsen & Johannes Muhle-Karbe, 2013. "The General Structure of Optimal Investment and Consumption with Small Transaction Costs," Papers 1303.3148, arXiv.org, revised May 2015.
    10. Detemple, Jerome & Sundaresan, Suresh, 1999. "Nontraded Asset Valuation with Portfolio Constraints: A Binomial Approach," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 835-872.
    11. John Y. Campbell & Yeung Lewis Chanb & M. Viceira, 2013. "A multivariate model of strategic asset allocation," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part II, chapter 39, pages 809-848, World Scientific Publishing Co. Pte. Ltd..
    12. 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.
    13. He, Xue-Zhong & Li, Youwei, 2015. "Testing of a market fraction model and power-law behaviour in the DAX 30," Journal of Empirical Finance, Elsevier, vol. 31(C), pages 1-17.
    14. Carpenter, Jennifer N., 1998. "The exercise and valuation of executive stock options," Journal of Financial Economics, Elsevier, vol. 48(2), pages 127-158, May.
    15. Lin, Wen-chang & Lu, Jin-ray, 2012. "Risky asset allocation and consumption rule in the presence of background risk and insurance markets," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 150-158.
    16. Li, Zhongfei & Yao, Jing & Li, Duan, 2010. "Behavior patterns of investment strategies under Roy's safety-first principle," The Quarterly Review of Economics and Finance, Elsevier, vol. 50(2), pages 167-179, May.
    17. Wolfgang Stummer, 2002. "Some Potential Means for Venture Valuation," Journal of Entrepreneurial Finance, Pepperdine University, Graziadio School of Business and Management, vol. 7(3), pages 39-52, Fall.
    18. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    19. Mark Davis & SEBastien Lleo, 2008. "Risk-sensitive benchmarked asset management," Quantitative Finance, Taylor & Francis Journals, vol. 8(4), pages 415-426.
    20. 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.

    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:fininn:v:3:y:2017:i:1:d:10.1186_s40854-017-0080-y. 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.