In this paper we construct robust models for active portfolio management ?in a market with transaction costs. The goal of these robust models is to control the impact of estimation errors in the values parameters on the performance of the portfolio strategy. Our models can handle a large class of piecewise convex transaction cost functions and allow one to impose additional side constraints such as bounds on the portfolio holdings, constraints on the portfolio beta and limits on cash and industry exposure. We show that the optimal portfolios can be computed by solving second-order cone programs – a class of optimization problems with a worst case complexity (ie, solution cost) that is comparable to that for solving convex quadratic programs (such as the Markowitz portfolio selection problem). We tested our robust strategies on real market data from September 1989 to August 2007 imposing realistic transaction costs. In these tests, the proposed robust active portfolio management strategies significantly outpe formed the S&P500 index without a significant increase in volatility.