论文标题
分位数聚集的卷积界限
Convolution Bounds on Quantile Aggregation
论文作者
论文摘要
依赖性不确定性的分位数聚集在概率理论中具有悠久的历史，在金融，风险管理，统计和运营研究中的应用很广。利用最新的基于分位数风险度量的INF卷积的结果，我们为分位数聚集建立了新的分析界限，我们称之为卷积界限。卷积界限既统一了分位数聚集中可用的每个分析结果，又启发了我们对这些方法的理解。这些界限通常是最好的。此外，卷积界限易于计算，我们表明它们在许多相关情况下都很清晰。它们还允许对极端依赖结构的解释性。结果直接导致具有任意依赖性随机变量总和的分布的界限。我们在风险管理和经济学中讨论相关应用。
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.
