Robustness-based portfolio optimization under epistemic uncertainty

In this paper, we propose formulations and algorithms for robust portfolio optimization under both aleatory uncertainty (i.e., natural variability) and epistemic uncertainty (i.e., imprecise probabilistic information) arising from interval data. Epistemic uncertainty is represented using two approaches: (1) moment bounding approach and (2) likelihood-based approach. This paper first proposes a nested robustness-based portfolio optimization formulation using the moment bounding approach-based representation of epistemic uncertainty. The nested robust portfolio formulation is simple to implement; however, the computational cost is often high due to the epistemic analysis performed inside the optimization loop. A decoupled approach is then proposed to un-nest the robustness-based portfolio optimization from the analysis of epistemic variables to achieve computational efficiency. This paper also proposes a single-loop robust portfolio optimization formulation using the likelihood-based representation of epistemic uncertainty that completely separates the epistemic analysis from the portfolio optimization framework and thereby achieves further computational efficiency. The proposed robust portfolio optimization formulations are tested on real market data from five S&P 500 companies, and performance of the robust optimization models is discussed empirically based on portfolio return and risk.