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This paper focuses on a dynamic multi-asset mean-variance portfolio selectionproblem under model uncertainty. We develop a continuous time framework fortaking into account ambiguity aversion about both expected return rates andcorrelation matrix of the assets, and for studying the join effects onportfolio diversification. The dynamic setting allows us to consider timevarying ambiguity sets, which include the cases where the drift and correlationare estimated on a rolling window of historical data or when the investor takesinto account learning on the ambiguity. In this context, we prove a generalseparation principle for the associated robust control problem, which allows usto reduce the determination of the optimal dynamic strategy to the parametriccomputation of the minimal risk premium function. Our results provide ajustification for under-diversification, as documented in empirical studies andin the static models [16], [34]. Furthermore, we explicitly quantify the degreeof under-diversification in termsof correlation bounds and Sharpe ratiosproximities, and emphasize the different features induced by drift andcorrelation ambiguity. In particular, we show that an investor with a poorconfidence in the expected return estimation does not hold any risky asset, andon the other hand, trades only one risky asset when the level of ambiguity oncorrelation matrix is large. We also provide a complete picture of thediversification for the optimal robust portfolio in the three-asset case JELClassification: G11, C61 MSC Classification: 91G10, 91G80, 60H30

Portfolio diversification and model uncertainty: a robust dynamic mean-variance approach