Robust Markowitz mean-variance portfolio selection under ambiguous covariance matrix *

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
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01385585
Contributeur : Huyen Pham <>
Soumis le : samedi 11 mars 2017 - 17:59:44
Dernière modification le : mercredi 15 mars 2017 - 01:08:01

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  • HAL Id : hal-01385585, version 2
  • ARXIV : 1610.06805

Citation

Amine Ismail, Huyên Pham. Robust Markowitz mean-variance portfolio selection under ambiguous covariance matrix *. 2017. <hal-01385585v2>

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