{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,2]],"date-time":"2026-08-02T01:29:07Z","timestamp":1785634147662,"version":"3.56.0"},"reference-count":10,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2025,9,18]],"date-time":"2025-09-18T00:00:00Z","timestamp":1758153600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2026,3]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>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.<\/jats:p>","DOI":"10.1017\/jpr.2025.31","type":"journal-article","created":{"date-parts":[[2025,9,18]],"date-time":"2025-09-18T06:40:42Z","timestamp":1758177642000},"page":"91-95","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":2,"title":["A note on subadditivity of value at risks (VaRs): A new connection to comonotonicity"],"prefix":"10.1017","volume":"63","author":[{"given":"Yuri","family":"Imamura","sequence":"first","affiliation":[{"name":"Tokyo University of Science"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1350-4155","authenticated-orcid":false,"given":"Takashi","family":"Kato","sequence":"additional","affiliation":[{"name":"Association of Mathematical Finance Laboratory"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2025,9,18]]},"reference":[{"key":"S0021900225000312_ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2024.11.001"},{"key":"S0021900225000312_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2010.06.004"},{"key":"S0021900225000312_ref9","volume-title":"Quantitative Risk Management","author":"McNeil","year":"2005"},{"key":"S0021900225000312_ref8","doi-asserted-by":"crossref","unstructured":"[8] F\u00f6llmer, H. and Schied, A. (2016). Stochastic Finance: An Introduction in Discrete Time, 4th edn. De Gruyter, Berlin.","DOI":"10.1515\/9783110463453"},{"key":"S0021900225000312_ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2010.11.003"},{"key":"S0021900225000312_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2008.08.002"},{"key":"S0021900225000312_ref7","first-page":"176","volume-title":"Value at Risk and Beyond","author":"Embrechts","year":"1999"},{"key":"S0021900225000312_ref3","doi-asserted-by":"publisher","DOI":"10.1006\/jmva.1993.1064"},{"key":"S0021900225000312_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6687(02)00134-8"},{"key":"S0021900225000312_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6687(02)00135-X"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900225000312","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T01:25:37Z","timestamp":1775525137000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900225000312\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,18]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,3]]}},"alternative-id":["S0021900225000312"],"URL":"https:\/\/doi.org\/10.1017\/jpr.2025.31","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,18]]},"assertion":[{"value":"\u00a9 The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}