Details
| Original language | English |
|---|---|
| Pages (from-to) | 18-26 |
| Number of pages | 9 |
| Journal | Insurance: Mathematics and Economics |
| Volume | 81 |
| Early online date | 25 Apr 2018 |
| Publication status | Published - Jul 2018 |
| Externally published | Yes |
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.
Keywords
- Acceptance sets, Comonotonicity, Eligible assets, Expected Shortfall, Risk measures, Value at Risk
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Economics, Econometrics and Finance(all)
- Economics and Econometrics
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: Insurance: Mathematics and Economics, Vol. 81, 07.2018, p. 18-26.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Which eligible assets are compatible with comonotonic capital requirements?
AU - Koch-Medina, P.
AU - Munari, C.
AU - Svindland, G.
N1 - Publisher Copyright: © 2018 Elsevier B.V.
PY - 2018/7
Y1 - 2018/7
N2 - 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.
AB - 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.
KW - Acceptance sets
KW - Comonotonicity
KW - Eligible assets
KW - Expected Shortfall
KW - Risk measures
KW - Value at Risk
UR - http://www.scopus.com/inward/record.url?scp=85046811733&partnerID=8YFLogxK
U2 - 10.1016/j.insmatheco.2018.04.003
DO - 10.1016/j.insmatheco.2018.04.003
M3 - Article
VL - 81
SP - 18
EP - 26
JO - Insurance: Mathematics and Economics
JF - Insurance: Mathematics and Economics
SN - 0167-6687
ER -