The limitations of comonotonic additive risk measures: a literature review

TL;DR

This paper reviews the limitations of comonotonic additive risk measures, highlighting their incompatibility with key properties and demonstrating they cannot be surplus invariant, thus challenging their applicability in certain contexts.

Contribution

It provides a comprehensive review of the incompatibilities of comonotonic additive risk measures with fundamental properties and introduces new insights using the Choquet representation.

Findings

Comonotonic additive risk measures are incompatible with certain central properties.

Such risk measures cannot be surplus invariant.

The paper highlights limitations in the applicability of these measures.

Abstract

Risk measures satisfying the axiom of comonotonic additivity are extensively studied, arguably because of the plethora of results indicating interesting aspects of such risk measures. Recent research, however, has shown that this axiom is incompatible with central properties in specific contexts. In this paper, we present a literature review of these incompatibilities. In addition, we use the Choquet representation of comonotonic additive risk measures to show they cannot be surplus invariant.