Exponential Spectral Risk Measures

TL;DR

This paper explores exponential spectral risk measures, highlighting their intuitive properties, estimation methods via numerical quadrature, and the use of bootstrap for confidence intervals, especially effective with normally distributed losses.

Contribution

It introduces exponential spectral risk measures, analyzes their properties, and proposes numerical and bootstrap methods for their estimation and confidence interval construction.

Findings

Exponential spectral risk measures have intuitive properties.

Numerical quadrature effectively estimates these risk measures.

Bootstrap provides precise confidence intervals for normally distributed losses.

Abstract

Spectral risk measures are attractive risk measures as they allow the user to obtain risk measures that reflect their subjective risk-aversion. This paper examines spectral risk measures based on an exponential utility function, and finds that these risk measures have nice intuitive properties. It also discusses how they can be estimated using numerical quadrature methods, and how confidence intervals for them can be estimated using a parametric bootstrap. Illustrative results suggest that estimated exponential spectral risk measures obtained using such methods are quite precise in the presence of normally distributed losses.