On Coherent Risk Measures Induced by Convex Risk Measures

  • Zhiping Chen
  • Qianhui Hu


We study the close relationship between coherent risk measures and convex risk measures. Inspired by the obtained results, we propose a class of coherent risk measures induced by convex risk measures. The robust representation and minimization problem of the induced coherent risk measure are investigated. A new coherent risk measure, the Entropic Conditional Value-at-Risk (ECVaR), is proposed as a special case. We show how to apply the induced coherent risk measure to realistic portfolio selection problems. Finally, by comparing its out-of-sample performance with that of CVaR, entropic risk measure, as well as entropic value-at-risk, we carry out a series of empirical tests to demonstrate the practicality and superiority of the ECVaR measure in optimal portfolio selection.


Coherent risk measure Convex risk measure Entropic conditional value-at-risk Robust representation Portfolio selection 

Mathematics Subject Classification (2010)

62P05 91B30 91B28 


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This work was supported by the National Natural Science Foundation of China (Grant Numbers 71371152 and 11571270). The authors are grateful to the anonymous reviewers and the editor for their constructive comments, which have helped us to improve the paper significantly in both content and style.


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of Computing Science, School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anPeople’s Republic of China

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