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Convolution Bounds on Quantile Aggregation

Author

Listed:
  • Jose Blanchet
  • Henry Lam
  • Yang Liu
  • Ruodu Wang

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, 2020. "Convolution Bounds on Quantile Aggregation," Papers 2007.09320, arXiv.org, revised Apr 2024.
    • Handle: RePEc:arx:papers:2007.09320
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    References listed on IDEAS

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    Cited by:

    1. Yuyu Chen & Peng Liu & Yang Liu & Ruodu Wang, 2020. "Ordering and Inequalities for Mixtures on Risk Aggregation," Papers 2007.12338, arXiv.org, revised Jun 2021.
    2. Silvana Pesenti & Qiuqi Wang & Ruodu Wang, 2020. "Optimizing distortion riskmetrics with distributional uncertainty," Papers 2011.04889, arXiv.org, revised Feb 2022.

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