The conditional tail expectation CTE is an important actuarial risk measure and a useful tool in financial risk assessment. Under the classical assumption that the second moment of the loss variable is finite, the asymptotic normality of the nonparametric CTE estimator has already been established in the literature. The noted result, however, is not applicable when the loss variable follows any distribution with infinite second moment, which is a frequent situation in practice. With a help of extreme-value methodology, in this paper, we offer a solution to the problem by suggesting a new CTE estimator, which is applicable when losses have finite means but infinite variances.

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The main aim of this paper is to propose an alternative estimate of the distortion risk measure for heavy-tailed claims. Our approach is based on the result of Balkema and de Haan (1974) [3], and Pickands (1975) [22] for approximating the tail of the distribution by a generalized Pareto distribution. The asymptotic normality of the new estimator is established, and its performance illustrated by some results of simulation who shows the advantages of the new estimator over the estimator based on the classical extreme-value theory.

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