Annals of Operations Research

, Volume 254, Issue 1–2, pp 251–275 | Cite as

A quantitative comparison of risk measures

  • Alois PichlerEmail author
Original Paper


The choice of a risk measure reflects a subjective preference of the decision maker in many managerial or real world economic problem formulations. To assess the impact of personal preferences it is thus of interest to have comparisons with other risk measures at hand. This paper develops a framework for comparing different risk measures. We establish a one-to-one relationship between norms and risk measures, that is, we associate a norm with a risk measure and conversely, we use norms to recover a genuine risk measure. The methods allow tight comparisons of risk measures and tight lower and upper bounds for risk measures are made available whenever possible. In this way we present a general framework for comparing risk measures with applications in numerous directions.


Risk measures Dual representation Fenchel–Young inequality 

JEL Classification

90C15 60B05 62P05 



We would like to thank the editor of the journal and the referees for their commitment to assess and improve the paper.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Technische Universität Chemnitz, Fakultät für MathematikChemnitzGermany

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