Title: Portfolio diversification and model uncertainty: a robust dynamic mean-variance approach,
Abstract: This paper is concerned with a 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 effects on portfolio
diversification. We prove a separation principle for the associated robust
control problem, which allows 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. We explicitly quantify the degree of
under-diversification in terms of correlation and Sharpe ratio 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. This extends to the continuous-time setting the results obtained by
Garlappi, Uppal and Wang [13], and Liu and Zeng [24] in a one-period model. JEL
Classification: G11, C61 MSC Classification: 91G10, 91G80, 60H30