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Robust maximization of asymptotic growth

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Listed:
  • Kardaras, Constantinos
  • Robertson, Scott

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.

Suggested Citation

  • Kardaras, Constantinos & Robertson, Scott, 2012. "Robust maximization of asymptotic growth," LSE Research Online Documents on Economics 44994, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:44994
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    File URL: http://eprints.lse.ac.uk/44994/
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    References listed on IDEAS

    as
    1. Erhan Bayraktar & Ioannis Karatzas & Song Yao, 2009. "Optimal Stopping for Dynamic Convex Risk Measures," Papers 0909.4948, arXiv.org, revised Nov 2009.
    2. Daniel Fernholz & Ioannis Karatzas, 2010. "On optimal arbitrage," Papers 1010.4987, arXiv.org.
    3. Robert Fernholz, 2001. "Equity portfolios generated by functions of ranked market weights," Finance and Stochastics, Springer, vol. 5(4), pages 469-486.
    4. 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.
    5. Anne Gundel, 2005. "Robust utility maximization for complete and incomplete market models," Finance and Stochastics, Springer, vol. 9(2), pages 151-176, April.
    6. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    7. Alexander Schied, 2007. "Optimal investments for risk- and ambiguity-averse preferences: a duality approach," Finance and Stochastics, Springer, vol. 11(1), pages 107-129, January.
    8. Jörg Osterrieder & Thorsten Rheinländer, 2006. "Arbitrage Opportunities in Diverse Markets via a Non-equivalent Measure Change," Annals of Finance, Springer, vol. 2(3), pages 287-301, July.
    Full references (including those not matched with items on IDEAS)

    Citations

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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. 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.
    7. David Itkin & Martin Larsson, 2020. "Robust Asymptotic Growth in Stochastic Portfolio Theory under Long-Only Constraints," Papers 2009.08533, arXiv.org, revised Aug 2021.
    8. 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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    More about this item

    Keywords

    asymptotic growth rate; robustness; generalized martingale problem; optimal arbitrage;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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