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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
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    References listed on IDEAS

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    1. 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.
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    3. 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..
    4. 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.
    5. 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.
    6. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    7. 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.
    8. 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.
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    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.

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