Our primary aim is to find an estimate of the expected shortfall in various situations: (1) Nonparametric situation, when the probability distribution of the incurred loss is unknown, only satisfying some general conditions. Then, following [3], the expected shortfall can be expressed through a minimization of a well known quantile criterion and its numerical estimate is based on the empirical quantile functionof the loss. (2) The distribution function of the loss is known, but the loss can be contaminated by an additive measurement error: Estimating the expected shortfallin such a case exploits the concept of pseudo-capacities elaborated in [11] and [6] and its numerical value is based on the empirical quantile function of the suitable capacity. (3) The loss distribution can be contaminated by the heavy right tail with Pareto index > 1. The problem of interest is in this case to evaluate the effect of the Pareto index on the resulting expected shortfall.

翻译：我们的首要目标是在各种情况下寻找预期短缺的估计:(1) 非参数情况,当所发生损失的概率分布不明时,只能满足某些一般条件;然后,在[3]之后,预期短缺可以通过尽量减少众所周知的孔数标准来表示,其数字估计以损失的经验量函数为基础。 (2) 损失的分布功能是已知的,但损失可能受到添加剂测量错误的污染:估计这种情况的预期短缺利用了[11]和[6]中阐述的伪能力概念,其数字价值是以适当能力的经验量函数为依据的。 (3) 损失分布可能受到严重右尾巴的污染,Pareto指数 > 1. 在本案中,利益冲突问题在于评价Pareto指数对由此产生的预期短缺的影响。