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On The Consumption/Distribution Theorem Under The Long-Run Growth Criterion Subject To A Drawdown Constraint

Author

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  • MICHAEL J. KLASS

    (Departments of Statistics and Mathematics, 367 Evans Hall and 910 Evans Hall, UC Berkeley, Berkeley, California 94720-3860, USA)

  • KRZYSZTOF NOWICKI

    (Department of Statistics, Lund University, Box 743, S-220 07 Lund, Sweden)

Abstract

Consider any discrete time sequence of investment fortunes Fn which has a finite long-run growth rate $V(r, \lambda_*)=\lim_{n\to\infty}\frac{\ln F_n}{n}$ when subject to the present value capital drawdown constraint Fne-rn ≥ λ* max0≤k≤nFke-rk, where 0 ≤ λ*

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:13:y:2010:i:06:n:s0219024910006054
    DOI: 10.1142/S0219024910006054
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    References listed on IDEAS

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    1. Harry M. Markowitz, 2011. "Investment for the Long Run: New Evidence for an Old Rule," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 35, pages 495-508, World Scientific Publishing Co. Pte. Ltd..
    2. Romuald Elie & Nizar Touzi, 2008. "Optimal lifetime consumption and investment under a drawdown constraint," Finance and Stochastics, Springer, vol. 12(3), pages 299-330, July.
    3. Eckhard Platen, 2005. "On The Role Of The Growth Optimal Portfolio In Finance," Australian Economic Papers, Wiley Blackwell, vol. 44(4), pages 365-388, December.
    4. 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.
    5. Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276, July.
    6. Alexander, Gordon J. & Baptista, Alexandre M., 2006. "Portfolio selection with a drawdown constraint," Journal of Banking & Finance, Elsevier, vol. 30(11), pages 3171-3189, November.
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