2016/02/17 by Pablo Koch-Medina, Pablo Koch‐Medina, Cosimo Munari +4
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Capital Investment and Risk Analysis #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Probability (math.PR) #Risk Management (q-fin.RM) #Risk and Portfolio Optimization #math.PR #q-fin.RM
paper · pdf · doi:10.48550/arxiv.1602.05477
openalex publication_date 2016/02/17 · arxiv created 2021/01/20 · arxiv updated 2021/01/21 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
Within the context of capital adequacy, we study comonotonicity of risk measures in terms of the primitives of the theory: acceptance sets and eligible, or reference, assets. We show that comonotonicity cannot be characterized by the properties of the acceptance set alone and heavily depends on the choice of the eligible asset. In fact, in many important cases, comonotonicity is only compatible with risk-free eligible assets. The incompatibility with risky eligible assets is systematic whenever the acceptability criterion is based on Value at Risk or any convex distortion risk measure such as Expected Shortfall. These findings qualify and arguably call for a critical appraisal of the meaning and the role of comonotonicity within a capital adequacy context.