Norms Based on Generalized Expected-Shortfalls and Applications

TL;DR

This paper introduces a new class of generalized Expected-Shortfall norms based on distortion risk measures, providing a unified framework for risk assessment, portfolio optimization, and anomaly detection in financial data.

Contribution

It develops the mathematical duality theory for these norms and demonstrates their application in portfolio optimization and financial time series analysis.

Findings

Unified framework for risk quantification using generalized ES norms

Effective portfolio optimization with the new norms

Application in detecting anomalies in financial data

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.