In this article, we establish several deviations for convex and coherent entropic risk measures. Firstly, we provide several deviations for the two risk measures with respect to relative entropy. Secondly, we provide several deviations for the two risk measures with respect to parameters....

In this article, we provide an estimation and several asymptotic behaviors for the coherent entropic risk measure of compound Poisson process. We also establish an estimation for the coherent entropic risk measure of sum of i.i.d. random variables in virtue of Log-Sobolev inequality. As an...