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Norms Based on Generalized Expected-Shortfalls and Applications

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  • Shuyu Gong
  • Taizhong Hu
  • Zhenfeng Zou

Abstract

This paper proposes a novel class of generalized Expected-Shortfall (ES) norms constructed via distortion risk measures, establishing a unified analytical framework for risk quantification. The proposed norms extend conventional ES methodology by incorporating flexible distortion functions. Specifically, we develop the mathematical duality theory for generalized-ES norms to support portfolio optimization tasks, while demonstrating their practical utility through projection problem solutions. The generalizedES norms are also applied to detect anomalies of financial time series data.

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  • Shuyu Gong & Taizhong Hu & Zhenfeng Zou, 2025. "Norms Based on Generalized Expected-Shortfalls and Applications," Papers 2507.09444, arXiv.org.
    • Handle: RePEc:arx:papers:2507.09444
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    File URL: http://arxiv.org/pdf/2507.09444
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