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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 784715, 9 pages
Research Article

Distributionally Robust Return-Risk Optimization Models and Their Applications

1Faculty of Management and Economics, Dalian University of Technology, Dalian 116024, China
2School of Mathematics and Computer Sciences, Shanxi Normal University, Linfen 041004, China

Received 27 February 2014; Accepted 5 May 2014; Published 20 May 2014

Academic Editor: Ying Hu

Copyright © 2014 Li Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.