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