The use of expectiles in risk management has recently gathered remarkable momentum due to their excellent axiomatic and probabilistic properties. In particular, the class of elicitable law-invariant coherent risk measures only consists of expectiles. While the theory of expectile estimation at central levels is substantial, tail estimation at extreme levels has so far only been considered when the tail of the underlying distribution is heavy. This article is the first work to handle the short-tailed setting where the loss (e.g. negative log-returns) distribution of interest is bounded to the right and the corresponding extreme value index is negative. We derive an asymptotic expansion of tail expectiles in this challenging context under a general second-order extreme value condition, which allows to come up with two semiparametric estimators of extreme expectiles, and with their asymptotic properties in a general model of strictly stationary but weakly dependent observations. A simulation study and a real data analysis from a forecasting perspective are performed to verify and compare the proposed competing estimation procedures.

翻译：最近，随着期望分位数在风险管理中具有卓越的公理和概率特性的应用越来越广泛，召唤了极大的动力。特别是，教唆法律不变的相容风险度量只包含期望分位数。虽然中心水平期望分位数的理论是很丰富的，但极值水平期望分位数的估计，在现有文献中只限于重尾分布的情况。这是第一篇研究处理偏短尾设置的论文，其中损失（如负对数收益率）感兴趣的分布是向右界限制的，相应的极值索引为负。我们在这种具有挑战性的背景下推导出一种渐进扩张的极值期望分位数，其中根据第二阶段个体值分布的一般极限值条件，可以得出两种半参数估计极值期望分位数的方法，并且可以在严格稳态但弱相关观察模型中计算其渐近性质。进行了模拟研究和来自预测角度的真实数据分析，以验证和比较所提出的竞争估计程序。