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Which eligible assets are compatible with comonotonic capital requirements?


Koch-Medina, Pablo; Munari, Cosimo; Svindland, Gregor (2018). Which eligible assets are compatible with comonotonic capital requirements? Insurance: Mathematics and Economics, 81:18-26.

Abstract

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.

Abstract

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Economics and Econometrics
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Language:English
Date:July 2018
Deposited On:30 Aug 2018 08:00
Last Modified:29 Jul 2020 07:39
Publisher:Elsevier
ISSN:0167-6687
OA Status:Closed
Publisher DOI:https://doi.org/10.1016/j.insmatheco.2018.04.003
Other Identification Number:merlin-id:16716

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