论文标题
风险度量引起的可变性的参数测量
Parametric measures of variability induced by risk measures
论文作者
论文摘要
我们为可变性度量的比较理论提出了一个一般框架，特别关注最近引入的一参数差异差异差异和相互差异的差异，这些家族将详细探讨，并将其与广泛的已知和应用的量表间差异进行了比较。从数学的角度来看，我们的主要结果是在一些其他技术条件下，对称和共音可变性度量的表征是指向不足差异的混合物。此外，我们研究了指向预期的短缺和预测差异的偶数比较引起的随机顺序，并讨论了它们与扩张顺序的关系。从统计的角度来看，我们建立了自然估计量的渐近一致性和正态性，并为跨案例提供了拇指的规则。最后，我们研究了在各种经济方面的标准普尔500指数上考虑的可变性度量类别的经验行为，并根据引入的随机订单探索不同时间序列的可比性。
We present a general framework for a comparative theory of variability measures, with a particular focus on the recently introduced one-parameter families of inter-Expected Shortfall differences and inter-expectile differences, that are explored in detail and compared with the widely known and applied inter-quantile differences. From the mathematical point of view, our main result is a characterization of symmetric and comonotonic variability measures as mixtures of inter-Expected Shortfall differences, under a few additional technical conditions. Further, we study the stochastic orders induced by the pointwise comparison of inter-Expected Shortfall and inter-expectile differences, and discuss their relationship with the dilation order. From the statistical point of view, we establish asymptotic consistency and normality of the natural estimators and provide a rule of the thumb for cross-comparisons. Finally, we study the empirical behaviour of the considered classes of variability measures on the S&P 500 Index under various economic regimes, and explore the comparability of different time series according to the introduced stochastic orders.
