In this paper, we are interested in the generalization and improvement of the estimator of the conditional tail expectation (CTE) for a heavy-tailed distribution when the second moment is infinite. It is well known that classical estimators of the CTE are seriously biased under the second-order...

In this paper, we generalize the classical estimator of the reinsurance premium for heavy-tailed loss distributions with a kernel-type estimator. Since this estimator exhibits a bias, we propose its bias-reduced version by using a least-squares method. The asymptotic normality of the proposed...