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：由于期望分位数在公理和概率性质上的优越性，其在风险管理中的应用近年来取得显著进展。特别地，可激励、与风险度量相容的相干风险度量类仅由期望分位数构成。尽管中心水平期望分位数估计理论已较为成熟，但极端水平的尾部估计此前仅在底层分布具有重尾特征时被研究。本文首次探讨短尾情形——即感兴趣损失（如负对数收益率）分布右端有界且相应极值指数为负的情况。我们在一般二阶极值条件下推导了该挑战性情境中尾部期望分位数的渐近展开式，据此提出两个极端期望分位数的半参数估计量，并在严格平稳但弱相依观测数据的一般模型中建立其渐近性质。通过模拟研究与基于预测视角的实际数据分析，对所提出的竞争性估计程序进行了验证与比较。