Spectral Risk Measures: Properties and Limitations

TL;DR

This paper examines spectral risk measures, highlighting their properties and limitations, and emphasizes the importance of selecting appropriate utility functions for different risk assessment scenarios.

Contribution

It analyzes the properties of spectral risk measures based on exponential and power utilities, revealing their limitations and guiding better utility function choices.

Findings

Both exponential and power utility-based SRMs have significant limitations.

Users must carefully select utility functions matching their specific risk assessment problems.

Power SRMs require especially careful consideration due to their limitations.

Abstract

Spectral risk measures (SRMs) are risk measures that take account of user riskaversion, but to date there has been little guidance on the choice of utility function underlying them. This paper addresses this issue by examining alternative approaches based on exponential and power utility functions. A number of problems are identified with both types of spectral risk measure. The general lesson is that users of spectral risk measures must be careful to select utility functions that fit the features of the particular problems they are dealing with, and should be especially careful when using power SRMs.