Quantifying the degree of risk aversion of spectral risk measures

TL;DR

This paper introduces a functional to quantify how risk-averse spectral risk measures are, based on axioms like normalization and linearity, providing formulas and discussing their properties.

Contribution

It formalizes the degree of risk aversion in spectral risk measures using axioms, offering new formulas and insights into their properties.

Findings

Proposes a functional to measure risk aversion in spectral risk measures

Provides two formulas for the risk aversion functional

Discusses properties and interpretations of the functional

Abstract

I propose a functional on the space of spectral risk measures that quantifies their ``degree of risk aversion''. This quantification formalizes the idea that some risk measures are ``more risk-averse'' than others. I construct the functional using two axioms: a normalization on the space of CVaRs and a linearity axiom. I present two formulas for the functional and discuss several properties and interpretations.