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As defined in Entropic Value-at-Risk: A New Coherent Risk Measure (reference) by A.Ahmadi-Javid, the entropic value-at-risk (EVaR) of $x\in L_{M^{+}}$ with confidence level $1-\alpha$ is: $$EVaR_{1-\alpha}(X) := \inf_{z>0}\left\{z^{-1}\ln\left(\frac{M_{X}}{\alpha}\right)\right\}$$ where $M_X$ is the moment generating function.

I was wondering can EVaR fit in the framework of distortion risk measures? And in that case how to calculate the distortion function for EVaR?

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You may find the answer based on the Kusuoka representation of the EV@R given in the following papers:

Freddy Delbaen, Remark on the Paper "Entropic Value-at-Risk: A New Coherent Risk Measure" by Amir Ahmadi-Javid. https://arxiv.org/abs/1504.00640

Amir Ahmadi-JavidEmail authorAlois Pichler. An analytical study of norms and Banach spaces induced by the entropic value-at-risk. https://link.springer.com/article/10.1007/s11579-017-0197-9

See the equivalent form of this representation in Remark 4.16 of the second paper.

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  • $\begingroup$ Thank you so much for your information. I need first read carefully. $\endgroup$
    – Xinyuan
    Oct 14 '17 at 10:36

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