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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.00244 |
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| _version_ | 1866914698131144704 |
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| author | Zhou, Weimi Liu, Yong-Jin |
| author_facet | Zhou, Weimi Liu, Yong-Jin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00244 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Wasserstein Distributionally Robust Mean Semi-Absolute Deviation Portfolio Model: Robust Selection and Efficient Computation Zhou, Weimi Liu, Yong-Jin Optimization and Control 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. |
| title | On Wasserstein Distributionally Robust Mean Semi-Absolute Deviation Portfolio Model: Robust Selection and Efficient Computation |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2403.00244 |