Paper: arXiv 2212.13864

Authors: Samuel Solgon Santos, Marcelo Brutti Righi, Eduardo de Oliveira Horta

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.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a theoretical literature review on comonotonic additive risk measures along with a novel proof regarding surplus invariance using the Choquet representation. While mathematically sound and well-structured, it is entirely theoretical and lacks empirical backtesting or data analysis.

Research Flowchart

  flowchart TD
    A["Research Goal: Identify limitations of comonotonic additive risk measures"] --> B["Literature Review & Theoretical Analysis"]
    C["Inputs: Comonotonic Additivity Axiom & Multi-Asset Contexts"] --> B
    B --> D["Apply Choquet Representation Theorem"]
    D --> E["Findings: Incompatibility with central properties in specific contexts"]
    D --> F["Key Outcome: Proof that comonotonic additive risk measures cannot be surplus invariant"]