Robust First Order Stochastic Dominance in Portfolio Optimization

We use modern approach of stochastic dominance in portfolio optimization, where we want the portfolio to dominate a benchmark. Since the distribution of returns is often just estimated from data, we look for the worst distribution that differs from empirical distribution at maximum by a predefined value. First, we define in what sense the distribution is the worst for the first order stochastic dominance. We derive a robust stochastic dominance test for the first order stochastic dominance and find the worst-case distribution as the optimal solution of a non-linear maximization problem. We apply the derived optimization programs to real life data, specifically to returns of assets captured by Dow Jones Industrial Average, and we analyze the problems in detail using optimal solutions of the optimization programs with multiple setups.