分位数聚合的卷积界
Convolution Bounds on Quantile Aggregation
AI总结：
本文利用基于分位数风险度量的下确界卷积结果，提出分位数聚合的卷积界，统一并改进现有解析界，且易于计算并在多种情形下精确，可应用于风险管理和经济学。
摘要：
具有相依不确定性（dependence uncertainty）的分位数聚合在概率论中有着悠久的历史，并在金融、风险管理、统计学和运筹学中有广泛应用。利用最近关于基于分位数的风险度量的下确界卷积（inf-convolution）的结果，我们建立了新的分位数聚合的解析界，称之为卷积界（convolution bounds）。卷积界既统一了分位数聚合中所有可用的解析结果，也加深了我们对这些方法的理解。这些界在一般情况下是目前可用的最优界。此外，卷积界易于计算，并且我们证明它们在许多相关情形下是精确的（sharp）。它们还允许对极端相依结构进行可解释性分析。这些结果直接导出了具有任意相依性的随机变量之和的分布的界。我们讨论了在风险管理和经济学中的相关应用。
英文摘要：
Quantile aggregation with dependence uncertainty has a long history in probability theory with wide applications in finance, risk management, statistics, and operations research. Using a recent result on inf-convolution of quantile-based risk measures, we establish new analytical bounds for quantile aggregation which we call convolution bounds. Convolution bounds both unify every analytical result available in quantile aggregation and enlighten our understanding of these methods. These bounds are the best available in general. Moreover, convolution bounds are easy to compute, and we show that they are sharp in many relevant cases. They also allow for interpretability on the extremal dependence structure. The results directly lead to bounds on the distribution of the sum of random variables with arbitrary dependence. We discuss relevant applications in risk management and economics.
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