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Robust asymptotic growth in stochastic portfolio theory under long‐only constraints

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  • David Itkin
  • Martin Larsson

Abstract

We consider the problem of maximizing the asymptotic growth rate of an investor under drift uncertainty in the setting of stochastic portfolio theory (SPT). As in the work of Kardaras and Robertson we take as inputs (i) aMarkovian volatility matrix c(x)$c(x)$ and (ii) an invariant density p(x)$p(x)$ for the market weights, but we additionally impose long‐only constraints on the investor. Our principal contribution is proving a uniqueness and existence result for the class of concave functionally generated portfolios and developing a finite dimensional approximation, which can be used to numerically find the optimum. In addition to the general results outlined above, we propose the use of a broad class of models for the volatility matrix c(x)$c(x)$, which can be calibrated to data and, under which, we obtain explicit formulas of the optimal unconstrained portfolio for any invariant density.

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  • 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.
    • Handle: RePEc:bla:mathfi:v:32:y:2022:i:1:p:114-171
    DOI: 10.1111/mafi.12331
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    References listed on IDEAS

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    1. Karatzas, Ioannis & Ruf, Johannes, 2017. "Trading strategies generated by Lyapunov functions," LSE Research Online Documents on Economics 69177, London School of Economics and Political Science, LSE Library.
    2. Constantinos Kardaras & Scott Robertson, 2010. "Robust maximization of asymptotic growth," Papers 1005.3454, arXiv.org, revised Aug 2012.
    3. Fernholz, Robert, 1999. "On the diversity of equity markets," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 393-417, April.
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    5. 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.
    6. Cuchiero, Christa, 2019. "Polynomial processes in stochastic portfolio theory," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1829-1872.
    7. Tomoyuki Ichiba & Vassilios Papathanakos & Adrian Banner & Ioannis Karatzas & Robert Fernholz, 2009. "Hybrid Atlas models," Papers 0909.0065, arXiv.org, revised Apr 2011.
    8. Erhan Bayraktar & Yu-Jui Huang, 2011. "Robust maximization of asymptotic growth under covariance uncertainty," Papers 1107.2988, arXiv.org, revised Sep 2013.
    9. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29, January.
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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. Steven Campbell & Qien Song & Ting-Kam Leonard Wong, 2024. "Macroscopic properties of equity markets: stylized facts and portfolio performance," Papers 2409.10859, arXiv.org.

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