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Robust maximization of asymptotic growth

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  • Constantinos Kardaras
  • Scott Robertson

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].

Suggested Citation

  • Constantinos Kardaras & Scott Robertson, 2010. "Robust maximization of asymptotic growth," Papers 1005.3454, arXiv.org, revised Aug 2012.
    • Handle: RePEc:arx:papers:1005.3454
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    References listed on IDEAS

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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. Anne Gundel, 2005. "Robust utility maximization for complete and incomplete market models," Finance and Stochastics, Springer, vol. 9(2), pages 151-176, April.
    4. 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.
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    Cited by:

    1. Andrew L. Allan & Christa Cuchiero & Chong Liu & David J. Prömel, 2023. "Model‐free portfolio theory: A rough path approach," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 709-765, July.
    2. Kerem Ugurlu, 2019. "Robust Utility Maximization with Drift and Volatility Uncertainty," Papers 1909.05335, arXiv.org.
    3. Andrew L. Allan & Christa Cuchiero & Chong Liu & David J. Promel, 2021. "Model-free Portfolio Theory: A Rough Path Approach," Papers 2109.01843, arXiv.org, revised Oct 2022.
    4. Constantinos Kardaras & Scott Robertson, 2018. "Ergodic robust maximization of asymptotic growth," Papers 1801.06425, arXiv.org.
    5. David Itkin & Martin Larsson, 2021. "Open Markets and Hybrid Jacobi Processes," Papers 2110.14046, arXiv.org, revised Mar 2024.
    6. Kardaras, Constantinos & Robertson, Scott, 2021. "Ergodic robust maximization of asymptotic growth," LSE Research Online Documents on Economics 121039, London School of Economics and Political Science, LSE Library.
    7. Christa Cuchiero & Walter Schachermayer & Ting‐Kam Leonard Wong, 2019. "Cover's universal portfolio, stochastic portfolio theory, and the numéraire portfolio," Mathematical Finance, Wiley Blackwell, vol. 29(3), pages 773-803, July.
    8. Yu-Jui Huang & Li-Hsien Sun, 2023. "Partial Information Breeds Systemic Risk," Papers 2312.04045, arXiv.org, revised Dec 2023.
    9. David Itkin & Martin Larsson, 2020. "Robust Asymptotic Growth in Stochastic Portfolio Theory under Long-Only Constraints," Papers 2009.08533, arXiv.org, revised Aug 2021.
    10. David Itkin & Martin Larsson, 2022. "Robust asymptotic growth in stochastic portfolio theory under long‐only constraints," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 114-171, January.

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