English

Norms Based on Generalized Expected-Shortfalls and Applications

Risk Management 2025-07-15 v1

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.

Keywords

Cite

@article{arxiv.2507.09444,
  title  = {Norms Based on Generalized Expected-Shortfalls and Applications},
  author = {Shuyu Gong and Taizhong Hu and Zhenfeng Zou},
  journal= {arXiv preprint arXiv:2507.09444},
  year   = {2025}
}
R2 v1 2026-07-01T03:58:15.124Z