# What's the advantages of $EVaR$ over $CVaR$?

$CVaR$, 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.

• 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. – Xinyuan Wei Jul 9 '18 at 15:20