Convolution Bounds on Quantile Aggregation

• 成果类型: Article
• 署名作者: Blanchet, Jose; Lam, Henry; Liu, Yang; Wang, Ruodu
• 署名单位: Stanford University; Columbia University; The Chinese University of Hong Kong, Shenzhen; University of Waterloo
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2021.0765
• 发表日期: 2025
• 关键词: value-at-risk; distributionally robust optimization; worst-case value; sensitivity-analysis; model uncertainty; sharp bounds; inequalities; computation

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.