Applied Mathematics & Optimization

, Volume 79, Issue 3, pp 671–693 | Cite as

Closed-Form Optimal Portfolios of Distributionally Robust Mean-CVaR Problems with Unknown Mean and Variance

  • Jia Liu
  • Zhiping ChenEmail author
  • Abdel Lisser
  • Zhujia Xu


In this paper, we consider both one-period and multi-period distributionally robust mean-CVaR portfolio selection problems. We adopt an uncertainty set which considers the uncertainties in terms of both the distribution and the first two order moments. We use the parametric method and the dynamic programming technique to come up with the closed-form optimal solutions for both the one-period and the multi-period robust portfolio selection problems. Finally, we show that our approaches are efficient when compared with both normal based portfolio selection models, and robust approaches based on known moments.


Distributionally robust optimization Robust portfolio selection Nested risk measure Conditional value-at-risk Closed-form solution 



The authors are grateful to the editor and two anonymous referees for their insightful, constructive and detailed comments and suggestions, which have helped us to improve the paper significantly in both content and style. This research was supported by the National Natural Science Foundation of China under grant numbers 71371152 and 11571270, and Programme Cai Yuanpei under grant number 34593YE.


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Jia Liu
    • 1
    • 2
  • Zhiping Chen
    • 1
    Email author
  • Abdel Lisser
    • 2
  • Zhujia Xu
    • 1
  1. 1.Department of Computing Science, School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anPeople’s Republic of China
  2. 2.Laboratoire de Recherche en Informatique (LRI)Université Paris Sud - XIOrsay CedexFrance

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