Risk measures such as Conditional Value-at-Risk (CVaR) focus on extreme losses, where scarce tail data makes model error unavoidable. To hedge misspecification, one evaluates worst-case tail risk over an ambiguity set. Using Extreme Value Theory (EVT), we derive first-order asymptotics for worst-case tail risk for a broad class of tail-risk measures under standard ambiguity sets, including Wasserstein balls and $φ$-divergence neighborhoods. We show that robustification can alter the nominal tail asymptotic scaling as the tail level $β\to0$, leading to excess risk inflation. Motivated by this diagnostic, we propose a tail-calibrated ambiguity design that preserves the nominal tail asymptotic scaling while still guarding against misspecification. Under standard domain of attraction assumptions, we prove that the resulting worst-case risk preserves the baseline first-order scaling as $β\to0$, uniformly over key tuning parameters, and that a plug-in implementation based on consistent tail-index estimation inherits these guarantees. Synthetic and real-data experiments show that the proposed design avoids the severe inflation often induced by standard ambiguity sets.

翻译：诸如条件风险价值（CVaR）等风险度量关注极端损失，该区域尾部数据稀缺，模型误差不可避免。为对冲模型误设风险，通常在一个模糊集上评估最坏情况下的尾部风险。利用极值理论（EVT），我们推导了在标准模糊集（包括Wasserstein球和$φ$-散度邻域）下，一类广泛尾部风险度量的最坏情况尾部风险的一阶渐近性质。研究表明，随着尾部水平$β\to0$，鲁棒化过程可能改变名义尾部渐近标度，导致超额风险膨胀。基于此诊断分析，我们提出了一种尾部校准的模糊集设计方法，该方法能在防范模型误设的同时，保持名义尾部渐近标度不变。在标准的吸引域假设下，我们证明了所得到的最坏情况风险在$β\to0$时保持基线一阶标度，且该性质在关键调节参数上一致成立；同时，基于一致性尾部指数估计的插件实现方法能够继承这些理论保证。合成数据与真实数据实验表明，所提出的设计方法能够避免标准模糊集常引发的严重风险膨胀。