  In this paper we investigate a utility maximization problem with drift
uncertainty in a multivariate continuous-time Black-Scholes type financial
market which may be incomplete. We impose a constraint on the admissible
strategies that prevents a pure bond investment and we include uncertainty by
means of ellipsoidal uncertainty sets for the drift. Our main results consist
firstly in finding an explicit representation of the optimal strategy and the
worst-case parameter, secondly in proving a minimax theorem that connects our
robust utility maximization problem with the corresponding dual problem.
Thirdly, we show that, as the degree of model uncertainty increases, the
optimal strategy converges to a generalized uniform diversification strategy.
