Robust Multi-Objective Portfolio Optimization Using Bertsimas Method

Abstract: Portfolio optimization has been a major topic of research in finance, as it has a significant impact on investment profit. In this paper, we investigate the problem of data uncertainty in convex multi-objective portfolio optimization. We extend Bertsimas definition of the robustness to the multi-objective case, which has two important advantages over the previous solutions. First, by restricting the maximum number of coefficients that are allowed to deviate in each row of the uncertainty matrix, we control the conservatism of our results. This modification renders our problem more flexible. Second, by using box uncertainty to model a noisy environment, we obtain an optimization problem with linear uncertainty set. This second alteration makes the solution more favorable computationally compared with the earlier nonlinear methods. Finally, using MANOVA analysis, we derive the exact amount of uncertainty for which our solution outperforms the previous results.