The limitations of comonotonic additive risk measures: a literature review

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 properties that are central in specific contexts. In this paper, we present a literature review of these incompatibilities. Specifically, we highlight the conflict between comonotonic additivity and surplus invariance, eligible assets, elicitabilty, and dynamic consistency.