Data-Driven Wasserstein Distributionally Robust Optimization Problem Based on the Shortfall Risk Measure

Inspired by various approaches to ambiguity set construction in the data-driven Wasserstein DRO model, we extend the classical method by constructing the ambiguity set using the Wasserstein metric based on the utility-shortfall risk measure. We investigate the tractability of the resulting Wasserstein DRO problem. We transform the worst-case expectation problem into a finite-dimensional optimization problem for concave or convex piecewise linear loss functions. Additionally, we simulate the theoretical results in the A-share market. The strategy provided by the Wasserstein DRO model based on the shortfall risk measure outperforms both the 1/N investment strategy and the mean-variance investment strategy in this case, offering a promising approach to portfolio selection.