Central limit theorem and almost sure results for the empirical estimator of superquantiles/CVaR in the stationary case

In this paper, we show that the difference between empirical estimator and Conditional value-at-risk can be written as a simple partial sum + residual term. Starting from decomposition, prove central limit theorem some almost sure results for estimator, large class of stationary sequences. We also construct confidence interval with asymptotic level 1−α, study its coverage through two different sets simulation.