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Article: Characterizing a comonotonic random vector by the distribution of the sum of its components

TitleCharacterizing a comonotonic random vector by the distribution of the sum of its components
Authors
KeywordsComonotonicity
Convex order
Distortion function
Distortion risk measure
Stop-loss order
Issue Date2010
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/ime
Citation
Insurance: Mathematics And Economics, 2010, v. 47 n. 2, p. 130-136 How to Cite?
AbstractIn this article, we characterize comonotonicity and related dependence structures among several random variables by the distribution of their sum. First we prove that if the sum has the same distribution as the corresponding comonotonic sum, then the underlying random variables must be comonotonic as long as each of them is integrable. In the literature, this result is only known to be true if either each random variable is square integrable or possesses a continuous distribution function. We then study the situation when the distribution of the sum only coincides with the corresponding comonotonic sum in the tail. This leads to the dependence structure known as tail comonotonicity. Finally, by establishing some new results concerning convex order, we show that comonotonicity can also be characterized by expected utility and distortion risk measures. © 2010 Elsevier B.V.
Persistent Identifierhttp://hdl.handle.net/10722/125402
ISSN
2015 Impact Factor: 1.378
2015 SCImago Journal Rankings: 1.000
ISI Accession Number ID
Funding AgencyGrant Number
Research Grants Council of HKSARHKU701409P
University of Hong Kong200905159011
Funding Information:

The author wishes to thank the anonymous referee for several valuable comments and suggestions which significantly improved the manuscript, and acknowledges the support by Research Grants Council of HKSAR (Project No. HKU701409P) and the Seed Funding Programme for Basic Research of The University of Hong Kong (Project No. 200905159011).

References

 

DC FieldValueLanguage
dc.contributor.authorCheung, KCen_HK
dc.date.accessioned2010-10-31T11:29:22Z-
dc.date.available2010-10-31T11:29:22Z-
dc.date.issued2010en_HK
dc.identifier.citationInsurance: Mathematics And Economics, 2010, v. 47 n. 2, p. 130-136en_HK
dc.identifier.issn0167-6687en_HK
dc.identifier.urihttp://hdl.handle.net/10722/125402-
dc.description.abstractIn this article, we characterize comonotonicity and related dependence structures among several random variables by the distribution of their sum. First we prove that if the sum has the same distribution as the corresponding comonotonic sum, then the underlying random variables must be comonotonic as long as each of them is integrable. In the literature, this result is only known to be true if either each random variable is square integrable or possesses a continuous distribution function. We then study the situation when the distribution of the sum only coincides with the corresponding comonotonic sum in the tail. This leads to the dependence structure known as tail comonotonicity. Finally, by establishing some new results concerning convex order, we show that comonotonicity can also be characterized by expected utility and distortion risk measures. © 2010 Elsevier B.V.en_HK
dc.languageengen_HK
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/imeen_HK
dc.relation.ispartofInsurance: Mathematics and Economicsen_HK
dc.subjectComonotonicityen_HK
dc.subjectConvex orderen_HK
dc.subjectDistortion functionen_HK
dc.subjectDistortion risk measureen_HK
dc.subjectStop-loss orderen_HK
dc.titleCharacterizing a comonotonic random vector by the distribution of the sum of its componentsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0167-6687&volume=47&issue=2&spage=130&epage=136&date=2010&atitle=Characterizing+a+comonotonic+random+vector+by+the+distribution+of+the+sum+of+its+componentsen_HK
dc.identifier.emailCheung, KC: kccg@hku.hken_HK
dc.identifier.authorityCheung, KC=rp00677en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.insmatheco.2010.06.004en_HK
dc.identifier.scopuseid_2-s2.0-77955655106en_HK
dc.identifier.hkuros181905en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-77955655106&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume47en_HK
dc.identifier.issue2en_HK
dc.identifier.spage130en_HK
dc.identifier.epage136en_HK
dc.identifier.isiWOS:000281982000004-
dc.publisher.placeNetherlandsen_HK
dc.identifier.scopusauthoridCheung, KC=10038874000en_HK
dc.identifier.citeulike7377677-

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