Journal of Optimization Theory and Applications

, Volume 155, Issue 3, pp 1124–1128

Addendum to: Entropic Value-at-Risk: A New Coherent Risk Measure



This short addendum consists of two sections. The first provides proofs that were omitted in Ahmadi-Javid (J. Optim. Theory Appl., 2012) for the sake of brevity, and also demonstrates that the dual representation of the entropic value-at-risk, which is given in Ahmadi-Javid (J. Optim. Theory Appl., 2012) for the case of bounded random variables, holds for all random variables whose moment-generating functions exist everywhere. The second section provides a few corrections.


Chernoff inequality Coherent risk measure Conditional value-at-risk (CVaR) Convex optimization Cumulant-generating function Duality Entropic value-at-risk (EVaR) g-entropic risk measure Moment-generating function Relative entropy Stochastic optimization Stochastic programming Value-at-risk (VaR) 


  1. 1.
    Ahmadi-Javid, A.: Entropic value-at-risk: A new coherent risk measure. J. Optim. Theory Appl. (2012), this issue Google Scholar
  2. 2.
    Jeyakumar, V., Wolkowicz, H.: Generalizations of Slater’s constraint qualification for infinite convex programs. Math. Program., Ser. B 57, 85–101 (1992) MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Cheridito, P., Li, T.: Risk measures on Orlicz hearts. Math. Finance 19, 189–214 (2009) MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Industrial EngineeringAmirkabir University of Technology (Tehran Polytechnic)TehranIran

Personalised recommendations