  In this paper, we investigate the extreme-value methodology, to propose an
improved estimator of the conditional tail expectation ($CTE$) for a loss
distribution with a finite mean but infinite variance. The present work
introduces a new estimator of the $CTE$ based on the bias-reduced estimators of
high quantile for heavy-tailed distributions. The asymptotic normality of the
proposed estimator is established and checked, in a simulation study. Moreover,
we compare, in terms of bias and mean squared error, our estimator with the
known old estimator.
