Mathematical Methods of Operations Research

, Volume 87, Issue 2, pp 169–195 | Cite as

An exact solution to a robust portfolio choice problem with multiple risk measures under ambiguous distribution

  • Zhilin Kang
  • Zhongfei Li
Original Article


This paper proposes a unified framework to solve distributionally robust mean-risk optimization problem that simultaneously uses variance, value-at-risk (VaR) and conditional value-at-risk (CVaR) as a triple-risk measure. It provides investors with more flexibility to find portfolios in the sense that it allows investors to optimize a return-risk profile in the presence of estimation error. We derive a closed-form expression for the optimal portfolio strategy to the robust mean-multiple risk portfolio selection model under distribution and mean return ambiguity (RMP). Specially, the robust mean-variance, robust maximum return, robust minimum VaR and robust minimum CVaR efficient portfolios are all special instances of RMP portfolios. We analytically and numerically show that the resulting portfolio weight converges to the minimum variance portfolio when the level of ambiguity aversion is in a high value. Using numerical experiment with simulated data, we demonstrate that our robust portfolios under ambiguity are more stable over time than the non-robust portfolios.


Portfolio selection Multiple-risk measures Distribution ambiguity Minimum variance portfolio Robustness 

Mathematics Subject Classification

91G10 91B30 90C29 62G35 



The authors thank the editor and an anonymous referee for their insightful comments and suggestions which improved the quality of the paper. In addition, fruitful comments from Professor Shushang Zhu for an early version are much appreciated.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of MathematicsSun Yat-sen UniversityGuangzhouPeople’s Republic of China
  2. 2.Sun Yat-sen Business SchoolSun Yat-sen UniversityGuangzhouPeople’s Republic of China
  3. 3.Xinhua College of Sun Yat-sen UniversityGuangzhouPeople’s Republic of China
  4. 4.School of Mathematical ScienceHuaqiao UniversityFujianPeople’s Republic of China

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