On Wasserstein Distributionally Robust Mean Semi-Absolute Deviation Portfolio Model: Robust Selection and Efficient Computation

Abstract

This paper focuses on the Wasserstein distributionally robust mean-lower semi-absolute deviation (DR-MLSAD) model, where the ambiguity set is a Wasserstein ball centered on the empirical distribution of the training sample. This model can be equivalently transformed into a convex problem. We develop a robust Wasserstein profile inference (RWPI) approach to determine the size of the Wasserstein radius for DR-MLSAD model. We also design an efficient proximal point dual semismooth Newton (PpdSsn) algorithm for the reformulated equivalent model. In numerical experiments, we compare the DR-MLSAD model with the radius selected by the RWPI approach to the DR-MLSAD model with the radius selected by cross-validation, the sample average approximation (SAA) of the MLSAD model, and the 1/N strategy on the real market datasets. Numerical results show that our model has better out-of-sample performance in most cases. Furthermore, we compare PpdSsn algorithm with first-order algorithms and Gurobi solver on random data. Numerical results verify the effectiveness of PpdSsn in solving large-scale DR-MLSAD problems.