Robust Multi-Objective Portfolio Optimization Using Bertsimas Method

TL;DR

This paper extends Bertsimas' robust optimization approach to multi-objective portfolio optimization, improving flexibility and computational efficiency while effectively managing data uncertainty.

Contribution

It introduces a multi-objective robust optimization framework with controlled conservatism and linear uncertainty modeling, enhancing computational tractability and practical applicability.

Findings

The method controls the level of conservatism in the solution.

Linear uncertainty sets improve computational efficiency.

MANOVA analysis identifies the uncertainty threshold where the approach outperforms previous methods.

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.