The classical Markowitz approach to portfolio selection is compromised by two major shortcomings. First, there is considerable model risk with respect to the distribution of asset returns. Particularly, mean returns are notoriously difficult to estimate. Moreover, the Markowitz approach is static in that it does not account for the possibility of portfolio rebalancing within the investment horizon. We propose a robust dynamic portfolio optimization model to overcome both shortcomings. The model arises from an infinite-dimensional min-max framework. The objective is to minimize the worst-case portfolio variance over a family of dynamic investment strategies subject to a return target constraint. The worst-case variance is evaluated with respect to a set of conceivable return distributions. We develop a quantitative approach to approximate this intractable problem by a tractable one and report on numerical experiments.