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A note on the statistical robustness of risk measures

机译：关于风险度量的统计稳健性的说明

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摘要

The question of robustness in risk measurement emerged only fairly recently, but it has already attracted considerable attention. The problem has been studied using various approaches, and several methods aiming at robustifying the risk measures have been proposed. However, a general robustness theory is still missing. We focus on the parametric estimators of risk measures and use Hampel's infinitesimal approach to derive the robustness properties. We derive the influence functions for the general parametric estimators of the value-at-risk and expected shortfall. For various distributions, the classical estimators, such as maximum likelihood, have unbounded influence functions and are not robust. Using the expression for the influence function, we propose a general strategy to construct robust estimators and explore their properties. The use of the methodology is demonstrated through several illustrative examples. Finally, we discuss an operational risk application and highlight the importance of the complementary information provided by nonrobust and robust estimates for regulatory capital calculation.
机译：风险度量的鲁棒性问题只是在最近才出现的，但是已经引起了相当大的关注。已经使用各种方法研究了该问题，并且已经提出了几种旨在加强风险措施的方法。但是，仍然缺少通用的鲁棒性理论。我们专注于风险度量的参数估计量，并使用Hampel的无穷小方法得出鲁棒性。我们推导了风险价值和预期缺口的一般参数估计量的影响函数。对于各种分布，经典的估计量（例如最大似然）具有无限的影响函数，并且不鲁棒。使用影响函数的表达式，我们提出了构造稳健估计量并探索其性质的一般策略。通过几个说明性示例演示了该方法的使用。最后，我们讨论了操作风险应用程序，并强调了非稳健估算提供的补充信息对于监管资本计算的重要性。

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