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A note on subadditivity of value at risks (VaRs): A new connection to comonotonicity

Part of: Applications Mathematical finance

Published online by Cambridge University Press:  18 September 2025

Yuri Imamura  and
Takashi Kato Open the ORCID record for Takashi Kato [Opens in a new window]
Yuri Imamura*
Affiliation:
Tokyo University of Science
Takashi Kato*
Affiliation:
Association of Mathematical Finance Laboratory
*
*Postal address: Department of Business Economics, School of Management, Tokyo University of Science, 1–11–2, Fujimi, Chiyoda-ku, Tokyo 102-0071, Japan. Email address: imamuray@rs.tus.ac.jp
**Postal address: 2-2-15, Minamiaoyama, Minato-ku, Tokyo 107-0062, Japan. Email address: takashi.kato@mathfi-lab.com
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Abstract

In this paper, we provide a new property of value at risk (VaR), which is a standard risk measure that is widely used in quantitative financial risk management. We show that the subadditivity of VaR for given loss random variables holds for any confidence level if and only if those are comonotonic. This result also gives a new equivalent condition for the comonotonicity of random vectors.

Keywords

Value at risk (VaR)risk measuresquantitative risk managementcomonotonicity

MSC classification

Primary: 91G70: Statistical methods, econometrics
Secondary: 62P05: Applications to actuarial sciences and financial mathematics

Information

Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 5
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust

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