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

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