Entropy–Mean–Upper Partial Deviation–Absolute Deviation Portfolio Problem and Its Wasserstein Distributionally Robust Counterpart

This paper proposes an Entropy–Mean–Upper partial deviation–Absolute Deviation (EMUAD) portfolio problem, introducing entropy to reduce investment risk and enhance portfolio diversification while simultaneously considering metrics such as mean return, upper partial deviation, and absolute deviation. To overcome the instability of empirical distributions, EMUAD is extended into a distributionally robust optimization portfolio problem (DR-EMUAD), which constructs a Wasserstein ambiguity set centered on the empirical distribution using the Wasserstein distance. Moreover, by applying suitable approximation methods, we obtained a convex version of DR-EUMAD. The Robust Wasserstein Profile Inference (RWPI) method is utilized to effectively determine the radius of the Wasserstein ambiguity set. To ensure practical applicability, we embed a comprehensive set of real-world constraints—industry exposure limits, position size bounds, an explicit turnover cap, and a liquidity-driven transaction-cost budget. Numerical experiments demonstrate that both EMUAD and DR-EMUAD outperform traditional portfolio problems, with DR-EMUAD particularly effective at controlling return volatility, significantly enhancing robustness and practical utility in investment decision-making.