Marginal expected shortfall is unquestionably one of the most popular systemic risk measures. Studying its extreme behaviour is particularly relevant for risk protection against severe global financial market downturns. In this context, results of statistical inference rely on the bivariate extreme values approach, disregarding the extremal dependence among a large number of financial institutions that make up the market. In order to take it into account we propose an inferential procedure based on the multivariate regular variation theory. We derive an approximating formula for the extreme marginal expected shortfall and obtain from it an estimator and its bias-corrected version. Then, we show their asymptotic normality, which allows in turn the confidence intervals derivation. Simulations show that the new estimators greatly improve upon the performance of existing ones and confidence intervals are very accurate. An application to financial returns shows the utility of the proposed inferential procedure. Statistical results are extended to a general $\beta$-mixing context that allows to work with popular time series models with heavy-tailed innovations.

翻译：边际预期损失无疑是最受欢迎的系统性风险度量之一。研究其极端行为对于防范全球金融市场严重下行的风险尤为重要。在此背景下，统计推断的结果依赖于二元极值方法，而忽略了构成市场的众多金融机构之间的极端依赖关系。为考虑这一关系，我们提出了一种基于多元正则变异理论的推断程序。我们推导出极端边际预期损失的近似公式，并据此得到其估计量及其偏差修正版本。随后，我们证明了它们的渐近正态性，从而可以推导出置信区间。模拟表明，新估计量相比现有估计量性能显著提升，且置信区间非常精确。一项对金融收益的实证分析展示了所提出的推断程序的实用性。统计结果被推广到一般的β-混合情形，这使得我们能够处理具有重尾新息的热门时间序列模型。