IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v13y2010i06ns0219024910006054.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024910006054
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024910006054?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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..
    3. Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276, July.
    4. 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.
    5. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    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. 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. Zabarankin, Michael & Pavlikov, Konstantin & Uryasev, Stan, 2014. "Capital Asset Pricing Model (CAPM) with drawdown measure," European Journal of Operational Research, Elsevier, vol. 234(2), pages 508-517.
    4. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, September.
    5. Drenovak, Mikica & Ranković, Vladimir & Urošević, Branko & Jelic, Ranko, 2022. "Mean-Maximum Drawdown Optimization of Buy-and-Hold Portfolios Using a Multi-objective Evolutionary Algorithm," Finance Research Letters, Elsevier, vol. 46(PA).
    6. Wang, Wenyuan & Chen, Ping & Li, Shuanming, 2020. "Generalized expected discounted penalty function at general drawdown for Lévy risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 12-25.
    7. Steven D. Moffitt, 2018. "Why Markets are Inefficient: A Gambling "Theory" of Financial Markets For Practitioners and Theorists," Papers 1801.01948, arXiv.org.
    8. Truc Le & Eckhard Platen, 2006. "Approximating the Growth Optimal Portfolio with a Diversified World Stock Index," Research Paper Series 184, Quantitative Finance Research Centre, University of Technology, Sydney.
    9. Alexander, Gordon J. & Baptista, Alexandre M., 2009. "Stress testing by financial intermediaries: Implications for portfolio selection and asset pricing," Journal of Financial Intermediation, Elsevier, vol. 18(1), pages 65-92, January.
    10. Jean-Pierre Fouque & Ruimeng Hu, 2016. "Asymptotic Optimal Strategy for Portfolio Optimization in a Slowly Varying Stochastic Environment," Papers 1603.03538, arXiv.org, revised Nov 2016.
    11. Sagara Dewasurendra & Pedro Judice & Qiji Zhu, 2019. "The Optimum Leverage Level of the Banking Sector," Risks, MDPI, vol. 7(2), pages 1-30, May.
    12. Ankush Agarwal & Ronnie Sircar, 2017. "Portfolio Benchmarking under Drawdown Constraint and Stochastic Sharpe Ratio," Working Papers hal-01388399, HAL.
    13. Muteba Mwamba, John & Suteni, Mwambi, 2010. "An alternative to portfolio selection problem beyond Markowitz’s: Log Optimal Growth Portfolio," MPRA Paper 50240, University Library of Munich, Germany.
    14. Chung-Han Hsieh & B. Ross Barmish, 2017. "On Drawdown-Modulated Feedback Control in Stock Trading," Papers 1710.01503, arXiv.org.
    15. Yong, Luo & Bo, Zhu & Yong, Tang, 2013. "Dynamic optimal capital growth with risk constraints," Economic Modelling, Elsevier, vol. 30(C), pages 586-594.
    16. Leonie Violetta Brinker, 2021. "Minimal Expected Time in Drawdown through Investment for an Insurance Diffusion Model," Risks, MDPI, vol. 9(1), pages 1-18, January.
    17. Bahman Angoshtari & Erhan Bayraktar & Virginia R. Young, 2018. "Optimal Dividend Distribution Under Drawdown and Ratcheting Constraints on Dividend Rates," Papers 1806.07499, arXiv.org, revised Mar 2019.
    18. Schuhmacher, Frank & Eling, Martin, 2011. "Sufficient conditions for expected utility to imply drawdown-based performance rankings," Journal of Banking & Finance, Elsevier, vol. 35(9), pages 2311-2318, September.
    19. Yuk-Loong Chow & Xiang Yu & Chao Zhou, 2020. "On Dynamic Programming Principle for Stochastic Control Under Expectation Constraints," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 803-818, June.
    20. Junbeom Lee & Xiang Yu & Chao Zhou, 2019. "Lifetime Ruin under High-watermark Fees and Drift Uncertainty," Papers 1909.01121, arXiv.org, revised Oct 2020.

    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:wsi:ijtafx:v:13:y:2010:i:06:n:s0219024910006054. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.