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The Grossman and Zhou investment strategy is not always optimal

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  • Klass, Michael J.
  • Nowicki, Krzysztof

Abstract

Grossman and Zhou [1993. Optimal investment strategies for controlling drawdowns. Math. Finance 3, 241-276] proposed a strategy to maximize the asymptotic long-run growth rate of one's fortune Ft subject to its never falling below , where 0[less-than-or-equals, slant][lambda][less-than-or-equals, slant]1 is a fixed constant chosen by the investor and r is a fixed, known, non-negative, continuously compounded interest rate on invested capital. In this paper we show that the strategy proposed in Grossman and Zhou does not retain its optimal long-run growth property when generalized to the discrete-time setting.

Suggested Citation

  • Klass, Michael J. & Nowicki, Krzysztof, 2005. "The Grossman and Zhou investment strategy is not always optimal," Statistics & Probability Letters, Elsevier, vol. 74(3), pages 245-252, October.
    • Handle: RePEc:eee:stapro:v:74:y:2005:i:3:p:245-252
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    References listed on IDEAS

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    1. Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276, July.
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    Cited by:

    1. Chen, Xinfu & Landriault, David & Li, Bin & Li, Dongchen, 2015. "On minimizing drawdown risks of lifetime investments," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 46-54.
    2. Vladimir Cherny & Jan Obłój, 2013. "Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial model," Finance and Stochastics, Springer, vol. 17(4), pages 771-800, October.
    3. Steven D. Moffitt, 2018. "Why Markets are Inefficient: A Gambling "Theory" of Financial Markets For Practitioners and Theorists," Papers 1801.01948, arXiv.org.
    4. Chung-Han Hsieh & B. Ross Barmish, 2017. "On Drawdown-Modulated Feedback Control in Stock Trading," Papers 1710.01503, arXiv.org.
    5. Michael J. Klass & Krzysztof Nowicki, 2010. "On The Consumption/Distribution Theorem Under The Long-Run Growth Criterion Subject To A Drawdown Constraint," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(06), pages 931-957.

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