IDEAS home Printed from
   My bibliography  Save this paper

Minimizing the Probability of Lifetime Drawdown under Constant Consumption


  • Bahman Angoshtari
  • Erhan Bayraktar
  • Virginia R. Young


We assume that an individual invests in a financial market with one riskless and one risky asset, with the latter's price following geometric Brownian motion as in the Black-Scholes model. Under a constant rate of consumption, we find the optimal investment strategy for the individual who wishes to minimize the probability that her wealth drops below some fixed proportion of her maximum wealth to date, the so-called probability of {\it lifetime drawdown}. If maximum wealth is less than a particular value, $m^*$, then the individual optimally invests in such a way that maximum wealth never increases above its current value. By contrast, if maximum wealth is greater than $m^*$ but less than the safe level, then the individual optimally allows the maximum to increase to the safe level.

Suggested Citation

  • Bahman Angoshtari & Erhan Bayraktar & Virginia R. Young, 2015. "Minimizing the Probability of Lifetime Drawdown under Constant Consumption," Papers 1507.08713,, revised May 2016.
  • Handle: RePEc:arx:papers:1507.08713

    Download full text from publisher

    File URL:
    File Function: Latest version
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    1. Marcel Nutz & Jianfeng Zhang, 2012. "Optimal stopping under adverse nonlinear expectation and related games," Papers 1212.2140,, revised Sep 2015.
    2. 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.
    3. Erhan Bayraktar & Masahiko Egami, 2008. "An Analysis of Monotone Follower Problems for Diffusion Processes," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 336-350, May.
    4. Wang, Ting & Young, Virginia R., 2012. "Maximizing the utility of consumption with commutable life annuities," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 352-369.
    5. Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276.
    6. Constantinos Kardaras & Jan Obłój & Eckhard Platen, 2017. "The Numéraire Property And Long-Term Growth Optimality For Drawdown-Constrained Investments," Mathematical Finance, Wiley Blackwell, vol. 27(1), pages 68-95, January.
    7. Erhan Bayraktar & Virginia Young, 2011. "Proving regularity of the minimal probability of ruin via a game of stopping and control," Finance and Stochastics, Springer, vol. 15(4), pages 785-818, December.
    8. Bahman Angoshtari & Erhan Bayraktar & Virginia R. Young, 2015. "Optimal Investment to Minimize the Probability of Drawdown," Papers 1506.00166,, revised Feb 2016.
    9. Erhan Bayraktar & Virginia Young, 2007. "Correspondence between lifetime minimum wealth and utility of consumption," Finance and Stochastics, Springer, vol. 11(2), pages 213-236, April.
    10. Wang, Ting & Young, Virginia R., 2012. "Optimal commutable annuities to minimize the probability of lifetime ruin," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 200-216.
    11. Erhan Bayraktar & Yu-Jui Huang, 2010. "On the Multi-Dimensional Controller and Stopper Games," Papers 1009.0932,, revised Jan 2013.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Angoshtari, Bahman & Bayraktar, Erhan & Young, Virginia R., 2015. "Minimizing the expected lifetime spent in drawdown under proportional consumption," Finance Research Letters, Elsevier, vol. 15(C), pages 106-114.
    2. Asaf Cohen & Virginia R. Young, 2015. "Minimizing Lifetime Poverty with a Penalty for Bankruptcy," Papers 1509.01694,
    3. repec:wsi:wsbook:10078 is not listed on IDEAS

    More about this item

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D14 - Microeconomics - - Household Behavior - - - Household Saving; Personal Finance
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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:arx:papers:1507.08713. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators). General contact details of provider: .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.