  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.
