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Optimal portfolios of a long-term investor with floor or drawdown constraints

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  • Vladimir Cherny
  • Jan Obloj
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    Abstract

    We study the portfolio selection problem of a long-run investor who is maximising the asymptotic growth rate of her expected utility. We show that, somewhat surprisingly, it is essentially not affected by introduction of a floor constraint which requires the wealth process to dominate a given benchmark at all times. We further study the notion of long-run optimality of wealth processes via convergence of finite horizon value functions to the asymptotic optimal value. We characterise long-run optimality under floor and drawdown constraints.

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    File URL: http://arxiv.org/pdf/1305.6831
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1305.6831.

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    Date of creation: May 2013
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    Handle: RePEc:arx:papers:1305.6831

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    1. W. H. Fleming & S. J. Sheu, 2000. "Risk-Sensitive Control and an Optimal Investment Model," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 197-213.
    2. Grossman, Sanford J. & Vila, Jean-Luc, 1992. "Optimal Dynamic Trading with Leverage Constraints," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(02), pages 151-168, June.
    3. Paolo Guasoni & Scott Robertson, 2012. "Portfolios and risk premia for the long run," Papers 1203.1399, arXiv.org.
    4. Mark Davis & SEBastien Lleo, 2008. "Risk-sensitive benchmarked asset management," Quantitative Finance, Taylor & Francis Journals, vol. 8(4), pages 415-426.
    5. Dumas, Bernard & Luciano, Elisa, 1991. " An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs," Journal of Finance, American Finance Association, vol. 46(2), pages 577-95, June.
    6. Laurent Carraro & Nicole El Karoui & Jan Ob{\l}\'oj, 2009. "On Az\'ema-Yor processes, their optimal properties and the Bachelier-drawdown equation," Papers 0902.1328, arXiv.org, revised Sep 2012.
    7. Dybvig, Philip H & Rogers, L C G & Back, Kerry, 1999. "Portfolio Turnpikes," Review of Financial Studies, Society for Financial Studies, vol. 12(1), pages 165-95.
    8. Hakansson, Nils H., 1974. "Convergence to isoelastic utility and policy in multiperiod portfolio choice," Journal of Financial Economics, Elsevier, vol. 1(3), pages 201-224, September.
    9. Cox, John C. & Huang, Chi-fu, 1992. "A continuous-time portfolio turnpike theorem," Journal of Economic Dynamics and Control, Elsevier, vol. 16(3-4), pages 491-507.
    10. Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276.
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