Expected utility models in portfolio optimization is based on the assumption of complete knowledge of the distribution of random returns. In this paper, we relax this assumption to the knowledge of only the mean, covariance and support information. No additional assumption on the type of distribution such as normality is made. The investor’s utility is modeled as a piecewise-linear concave function. We derive exact and approximate optimal trading strategies for a robust or maximin expected utility model, where the investor maximizes his worst case expected utility over a set of ambiguous distributions. The optimal portfolios are identified using a tractable conic programming approach. Using the optimized certainty equivalent (OCE) framework of Ben-Tal and Teboulle , we provide connections of our results with robust or ambiguous convex risk measures, in which the investor minimizes his worst case risk under distributional ambiguity. New closed form expressions for the OCE risk measures and optimal portfolios are provided for two and three piece utility functions. Computational experiments indicate that such robust approaches can provide good trading strategies in financial markets.