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Robust Markowitz mean-variance portfolio selection under ambiguous covariance matrix

Author

Listed:
  • Amine Ismail

    (LPMA)

  • Huy^en Pham

    (LPMA, CREST)

Abstract

This paper studies a robust continuous-time Markowitz portfolio selection pro\-blem where the model uncertainty carries on the covariance matrix of multiple risky assets. This problem is formulated into a min-max mean-variance problem over a set of non-dominated probability measures that is solved by a McKean-Vlasov dynamic programming approach, which allows us to characterize the solution in terms of a Bellman-Isaacs equation in the Wasserstein space of probability measures. We provide explicit solutions for the optimal robust portfolio strategies and illustrate our results in the case of uncertain volatilities and ambiguous correlation between two risky assets. We then derive the robust efficient frontier in closed-form, and obtain a lower bound for the Sharpe ratio of any robust efficient portfolio strategy. Finally, we compare the performance of Sharpe ratios for a robust investor and for an investor with a misspecified model. MSC Classification: 91G10, 91G80, 60H30

Suggested Citation

  • Amine Ismail & Huy^en Pham, 2016. "Robust Markowitz mean-variance portfolio selection under ambiguous covariance matrix ," Papers 1610.06805, arXiv.org, revised Mar 2017.
    • Handle: RePEc:arx:papers:1610.06805
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    File URL: http://arxiv.org/pdf/1610.06805
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    References listed on IDEAS

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    1. Larry G. Epstein & Shaolin Ji, 2013. "Ambiguous Volatility and Asset Pricing in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 26(7), pages 1740-1786.
    2. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    3. Karandikar, Rajeeva L., 1995. "On pathwise stochastic integration," Stochastic Processes and their Applications, Elsevier, vol. 57(1), pages 11-18, May.
    4. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
    5. T. J. Lyons, 1995. "Uncertain volatility and the risk-free synthesis of derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 117-133.
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    Cited by:

    1. Huyên Pham & Xiaoli Wei & Chao Zhou, 2021. "Portfolio diversification and model uncertainty: a robust dynamic mean-variance approach," Working Papers hal-01867133, HAL.
    2. Huyen Pham & Xiaoli Wei & Chao Zhou, 2018. "Portfolio diversification and model uncertainty: a robust dynamic mean-variance approach," Papers 1809.01464, arXiv.org, revised Dec 2021.
    3. Carmine de Franco & Johann Nicolle & Huyên Pham, 2018. "Bayesian learning for the Markowitz portfolio selection problem," Working Papers hal-01923917, HAL.
    4. Carmine De Franco & Johann Nicolle & Huy^en Pham, 2018. "Bayesian learning for the Markowitz portfolio selection problem," Papers 1811.06893, arXiv.org.

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