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$CVaR$, which is short for Conditional Value-at-Risk, has long been accepted by both academe and practice as a good coherent risk measure. Entropic value-at-risk ($EVaR$) is a comparative new coherent risk measure compared to $CVaR$.

What is the advantages of $EVaR$ over $CVaR$? Or in what situation, $EVaR$ would perform better than $CVaR$?

Here $EVaR$ is defined as, $$ \text{EVaR}_{1-\alpha}(X) := \inf_{z>0}\{z^{-1}ln(M_{X}(z))/\alpha\}= \inf_{z>0}\{z^{-1}ln(e^{-z*X}/\alpha\}. $$

Ahmadi-Javid, Amir. "Entropic value-at-risk: A new coherent risk measure." Journal of Optimization Theory and Applications 155.3 (2012): 1105-1123.

https://link.springer.com/article/10.1007%2Fs10957-011-9968-2

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    $\begingroup$ Welcome! Could you give us the definition of EVaR? The link to a page that charges to get the info is not optimal. What do you already know about this risk measure? $\endgroup$ – Richard Jul 9 '18 at 10:17
  • $\begingroup$ Isn't the answer to your question precisely in the research paper you linked ? $\endgroup$ – Lliane Jul 9 '18 at 14:35
  • $\begingroup$ Thank you for your interest. Entropic Value-at-Risk (EVaR) was first introduced by A. Ahmadi-Javid. The entropic value-at-risk of $X \in L_{M^{+}}$ with confidence level $1-\alpha$ is defined as: $$ \text{EVaR}_{1-\alpha}(X) := \inf_{z>0}\{z^{-1}ln(M_{X}(z))/\alpha\}= \inf_{z>0}\{z^{-1}ln(e^{-z*X}/\alpha\}. $$ Ahmadi-Javid, Amir. "Entropic value-at-risk: A new coherent risk measure." Journal of Optimization Theory and Applications 155.3 (2012): 1105-1123. $\endgroup$ – Xinyuan Wei Jul 9 '18 at 15:20

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