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Convolution Bounds on Quantile Aggregation

Author

Listed:
  • Jose Blanchet

    (Department of Management Science and Engineering, Stanford University, Stanford, California 94305)

  • Henry Lam

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

  • Yang Liu

    (School of Science and Engineering, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong 518172, China)

  • Ruodu Wang

    (Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada)

Abstract

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.

Suggested Citation

  • Jose Blanchet & Henry Lam & Yang Liu & Ruodu Wang, 2025. "Convolution Bounds on Quantile Aggregation," Operations Research, INFORMS, vol. 73(5), pages 2761-2781, September.
    • Handle: RePEc:inm:oropre:v:73:y:2025:i:5:p:2761-2781
    DOI: 10.1287/opre.2021.0765
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