Estimations and asymptotic behaviors of coherent entropic risk measure for sums of random variables

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 application, we provide two deviation estimations of the tail probability for compound Poisson process. Finally, several simulation results are given to support our results.