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摘要翻译：
当从历史数据或蒙特卡罗模拟中估计P&L的风险时，估计的稳健性是重要的。本文认为Hampel的经典定性鲁棒性概念不适用于风险度量，并提出和分析了一个改进的鲁棒性概念，它适用于Orlicz空间上的尾相关律不变凸风险度量。这种鲁棒性的概念抓住了鲁棒性和灵敏度之间的折衷，并可以通过定性鲁棒性指标来量化。通过这一指标，我们可以比较各种风险度量，如失真风险度量，其稳健程度。我们的分析还得到了一些独立的结果，如风险测度估计量的连续性和相合性，或{\psi}-弱收敛的Skorohod表示定理。
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英文标题：
《Comparative and qualitative robustness for law-invariant risk measures》
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作者：
Volker Kr\"atschmer, Alexander Schied, Henryk Z\"ahle
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最新提交年份：
2014
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
When estimating the risk of a P&L from historical data or Monte Carlo simulation, the robustness of the estimate is important. We argue here that Hampel's classical notion of qualitative robustness is not suitable for risk measurement and we propose and analyze a refined notion of robustness that applies to tail-dependent law-invariant convex risk measures on Orlicz space. This concept of robustness captures the tradeoff between robustness and sensitivity and can be quantified by an index of qualitative robustness. By means of this index, we can compare various risk measures, such as distortion risk measures, in regard to their degree of robustness. Our analysis also yields results that are of independent interest such as continuity properties and consistency of estimators for risk measures, or a Skorohod representation theorem for {\psi}-weak convergence.
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PDF链接：
https://arxiv.org/pdf/1204.2458
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