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Robust maximization of asymptotic growth under covariance uncertainty

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  • Erhan Bayraktar
  • Yu-Jui Huang

Abstract

This paper resolves a question proposed in Kardaras and Robertson [Ann. Appl. Probab. 22 (2012) 1576-1610]: how to invest in a robust growth-optimal way in a market where precise knowledge of the covariance structure of the underlying assets is unavailable. Among an appropriate class of admissible covariance structures, we characterize the optimal trading strategy in terms of a generalized version of the principal eigenvalue of a fully nonlinear elliptic operator and its associated eigenfunction, by slightly restricting the collection of nondominated probability measures.

Suggested Citation

  • Erhan Bayraktar & Yu-Jui Huang, 2011. "Robust maximization of asymptotic growth under covariance uncertainty," Papers 1107.2988, arXiv.org, revised Sep 2013.
    • Handle: RePEc:arx:papers:1107.2988
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    File URL: http://arxiv.org/pdf/1107.2988
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    References listed on IDEAS

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    1. Daniel Fernholz & Ioannis Karatzas, 2010. "On optimal arbitrage," Papers 1010.4987, arXiv.org.
    2. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    3. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
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    Cited by:

    1. David Itkin & Martin Larsson, 2020. "Robust Asymptotic Growth in Stochastic Portfolio Theory under Long-Only Constraints," Papers 2009.08533, arXiv.org, revised Aug 2021.
    2. Constantinos Kardaras & Scott Robertson, 2018. "Ergodic robust maximization of asymptotic growth," Papers 1801.06425, arXiv.org.
    3. 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.
    4. Steven Campbell & Qien Song & Ting-Kam Leonard Wong, 2024. "Macroscopic properties of equity markets: stylized facts and portfolio performance," Papers 2409.10859, arXiv.org, revised Apr 2025.
    5. 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.
    6. Erhan Bayraktar & Alexander Munk, 2017. "Mini-Flash Crashes, Model Risk, and Optimal Execution," Papers 1705.09827, arXiv.org, revised Aug 2018.
    7. Marcel Nutz, 2013. "Utility Maximization under Model Uncertainty in Discrete Time," Papers 1307.3597, arXiv.org.

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