论文标题
在各种实验条件下的预期不足的估计
Estimation of Expected Shortfall under Various Experimental Conditions
论文作者
论文摘要
我们的主要目的是在各种情况下找到对预期不足的估计：（1）当未知的损失的概率分布是未知的，只能满足某些一般条件时，非参数情况。然后，之后[3]，可以通过最小化众所周知的分位数标准来表达预期的短缺，其数值估计基于损失的经验分位数。 （2）已知损失的分布函数，但是损失可能会被添加剂测量误差污染：估计预期的短缺这种情况会利用[11]和[6]和[6]及其数值及其数值基于合适能力的经验分位功能的伪容器的概念。 （3）损失分布可以被带有帕累托指数> 1的重右尾部污染。在这种情况下，感兴趣的问题是评估帕累托指数对产生的预期不足的影响。
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.
