Distributionally Robust Return-Risk Optimization Models and Their Applications
Based on the risk control of conditional value-at-risk, distributionally robust return-risk optimization models with box constraints of random vector are proposed. They describe uncertainty in both the distribution form and moments (mean and covariance matrix of random vector). It is difficult to so...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/784715 |
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| _version_ | 1850110399038357504 |
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| author | Li Yang Yanxi Li Zhengyong Zhou Kejing Chen |
| author_facet | Li Yang Yanxi Li Zhengyong Zhou Kejing Chen |
| author_sort | Li Yang |
| collection | DOAJ |
| description | Based on the risk control of conditional value-at-risk, distributionally robust return-risk optimization models with box constraints of random vector are proposed. They describe uncertainty in both the distribution form and moments (mean and covariance matrix of random vector). It is difficult to solve them directly. Using the conic duality theory and the minimax theorem, the models are reformulated as semidefinite programming problems, which can be solved by interior point algorithms in polynomial time. An important theoretical basis is therefore provided for applications of the models. Moreover, an application of the models to a practical example of portfolio selection is considered, and the example is evaluated using a historical data set of four stocks. Numerical results show that proposed methods are robust and the investment strategy is safe. |
| format | Article |
| id | doaj-art-4205f196d7fa40d294f6fd30891ff89f |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-4205f196d7fa40d294f6fd30891ff89f2025-08-20T02:37:51ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/784715784715Distributionally Robust Return-Risk Optimization Models and Their ApplicationsLi Yang0Yanxi Li1Zhengyong Zhou2Kejing Chen3Faculty of Management and Economics, Dalian University of Technology, Dalian 116024, ChinaFaculty of Management and Economics, Dalian University of Technology, Dalian 116024, ChinaSchool of Mathematics and Computer Sciences, Shanxi Normal University, Linfen 041004, ChinaFaculty of Management and Economics, Dalian University of Technology, Dalian 116024, ChinaBased on the risk control of conditional value-at-risk, distributionally robust return-risk optimization models with box constraints of random vector are proposed. They describe uncertainty in both the distribution form and moments (mean and covariance matrix of random vector). It is difficult to solve them directly. Using the conic duality theory and the minimax theorem, the models are reformulated as semidefinite programming problems, which can be solved by interior point algorithms in polynomial time. An important theoretical basis is therefore provided for applications of the models. Moreover, an application of the models to a practical example of portfolio selection is considered, and the example is evaluated using a historical data set of four stocks. Numerical results show that proposed methods are robust and the investment strategy is safe.http://dx.doi.org/10.1155/2014/784715 |
| spellingShingle | Li Yang Yanxi Li Zhengyong Zhou Kejing Chen Distributionally Robust Return-Risk Optimization Models and Their Applications Journal of Applied Mathematics |
| title | Distributionally Robust Return-Risk Optimization Models and Their Applications |
| title_full | Distributionally Robust Return-Risk Optimization Models and Their Applications |
| title_fullStr | Distributionally Robust Return-Risk Optimization Models and Their Applications |
| title_full_unstemmed | Distributionally Robust Return-Risk Optimization Models and Their Applications |
| title_short | Distributionally Robust Return-Risk Optimization Models and Their Applications |
| title_sort | distributionally robust return risk optimization models and their applications |
| url | http://dx.doi.org/10.1155/2014/784715 |
| work_keys_str_mv | AT liyang distributionallyrobustreturnriskoptimizationmodelsandtheirapplications AT yanxili distributionallyrobustreturnriskoptimizationmodelsandtheirapplications AT zhengyongzhou distributionallyrobustreturnriskoptimizationmodelsandtheirapplications AT kejingchen distributionallyrobustreturnriskoptimizationmodelsandtheirapplications |