Expectile, as the minimizer of an asymmetric quadratic loss function, is a coherent risk measure and is helpful to use more information about the distribution of the considered risk. In this paper, we propose a new risk measure by replacing quantiles by expectiles, called expectile-based conditional tail moment, and focus on the estimation of this new risk measure as the conditional survival function of the risk, given the risk exceeding the expectile and given a value of the covariates, is heavy tail. Under some regular conditions, asymptotic properties of this new estimator are considered. The extrapolated estimation of the conditional tail moments is also investigated. These results are illustrated both on simulated data and on a real insurance data.

翻译：期望分位数作为非对称二次损失函数的最小化器，是一种一致风险度量，有助于更充分地利用所考虑风险分布的信息。本文通过用期望分位数替代分位数，提出了一种新的风险度量——基于期望分位数的条件尾矩。鉴于在风险超过期望分位数且协变量值给定的条件下，风险的条件生存函数呈现重尾特征，本研究聚焦于该新风险度量的估计。在正则条件下，本文论证了该新估计量的渐近性质，并进一步探讨了条件尾矩的外推估计方法。模拟数据集与真实保险数据集上的实证结果验证了上述方法的有效性。