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Robust maximization of asymptotic growth

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  • Constantinos Kardaras
  • Scott Robertson
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    Abstract

    This paper addresses the question of how to invest in a robust growth-optimal way in a market where the instantaneous expected return of the underlying process is unknown. The optimal investment strategy is identified using a generalized version of the principal eigenfunction for an elliptic second-order differential operator, which depends on the covariance structure of the underlying process used for investing. The robust growth-optimal strategy can also be seen as a limit, as the terminal date goes to infinity, of optimal arbitrages in the terminology of Fernholz and Karatzas [Ann. Appl. Probab. 20 (2010) 1179-1204].

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    File URL: http://arxiv.org/pdf/1005.3454
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1005.3454.

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    Date of creation: May 2010
    Date of revision: Aug 2012
    Publication status: Published in Annals of Applied Probability 2012, Vol. 22, No. 4, 1576-1610
    Handle: RePEc:arx:papers:1005.3454

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    Web page: http://arxiv.org/

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    1. Robert Fernholz, 2001. "Equity portfolios generated by functions of ranked market weights," Finance and Stochastics, Springer, vol. 5(4), pages 469-486.
    2. Alexander Schied & Ching-Tang Wu, 2005. "Duality theory for optimal investments under model uncertainty," SFB 649 Discussion Papers SFB649DP2005-025, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Sep 2005.
    3. László Györfi & András Urbán & István Vajda, 2007. "Kernel-Based Semi-Log-Optimal Empirical Portfolio Selection Strategies," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(03), pages 505-516.
    4. Anne Gundel, 2005. "Robust utility maximization for complete and incomplete market models," Finance and Stochastics, Springer, vol. 9(2), pages 151-176, 04.
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