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We give explicit solutions for utility maximization of terminal wealth problemu(X_T ) in the presence of Knightian uncertainty in continuous time [0, T] in a completemarket. We assume there is uncertainty on both drift and volatility of the underlying stocks, which induce nonequivalent measures on canonical space of continuous pathsΩ. We take that the uncertainty set resides in compact sets that are time dependent.In this framework, we solve the robust optimization problem with logarithmic, powerand exponential utility functions, explicitly.