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Article: Upper comonotonicity and convex upper bounds for sums of random variables

TitleUpper comonotonicity and convex upper bounds for sums of random variables
Authors
KeywordsComonotonicity
Convex Order
Tail Dependence
Upper Comonotonicity
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. 159-166 How to Cite?
AbstractIt is well-known that if a random vector with given marginal distributions is comonotonic, it has the largest sum with respect to convex order. However, replacing the (unknown) copula by the comonotonic copula will in most cases not reflect reality well. For instance, in an insurance context we may have partial information about the dependence structure of different risks in the lower tail. In this paper, we extend the aforementioned result, using the concept of upper comonotonicity, to the case where the dependence structure of a random vector in the lower tail is already known. Since upper comonotonic random vectors have comonotonic behavior in the upper tail, we are able to extend several well-known results of comonotonicity to upper comonotonicity. As an application, we construct different increasing convex upper bounds for sums of random variables and compare these bounds in terms of increasing convex order. © 2010 Elsevier B.V.
Persistent Identifierhttp://hdl.handle.net/10722/172474
ISSN
2015 Impact Factor: 1.378
2015 SCImago Journal Rankings: 1.000
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorDong, Jen_US
dc.contributor.authorCheung, KCen_US
dc.contributor.authorYang, Hen_US
dc.date.accessioned2012-10-30T06:22:42Z-
dc.date.available2012-10-30T06:22:42Z-
dc.date.issued2010en_US
dc.identifier.citationInsurance: Mathematics And Economics, 2010, v. 47 n. 2, p. 159-166en_US
dc.identifier.issn0167-6687en_US
dc.identifier.urihttp://hdl.handle.net/10722/172474-
dc.description.abstractIt is well-known that if a random vector with given marginal distributions is comonotonic, it has the largest sum with respect to convex order. However, replacing the (unknown) copula by the comonotonic copula will in most cases not reflect reality well. For instance, in an insurance context we may have partial information about the dependence structure of different risks in the lower tail. In this paper, we extend the aforementioned result, using the concept of upper comonotonicity, to the case where the dependence structure of a random vector in the lower tail is already known. Since upper comonotonic random vectors have comonotonic behavior in the upper tail, we are able to extend several well-known results of comonotonicity to upper comonotonicity. As an application, we construct different increasing convex upper bounds for sums of random variables and compare these bounds in terms of increasing convex order. © 2010 Elsevier B.V.en_US
dc.languageengen_US
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/imeen_US
dc.relation.ispartofInsurance: Mathematics and Economicsen_US
dc.subjectComonotonicityen_US
dc.subjectConvex Orderen_US
dc.subjectTail Dependenceen_US
dc.subjectUpper Comonotonicityen_US
dc.titleUpper comonotonicity and convex upper bounds for sums of random variablesen_US
dc.typeArticleen_US
dc.identifier.emailCheung, KC: kccg@hku.hken_US
dc.identifier.emailYang, H: hlyang@hku.hken_US
dc.identifier.authorityCheung, KC=rp00677en_US
dc.identifier.authorityYang, H=rp00826en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1016/j.insmatheco.2010.05.006en_US
dc.identifier.scopuseid_2-s2.0-77955655390en_US
dc.identifier.hkuros170572-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-77955655390&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume47en_US
dc.identifier.issue2en_US
dc.identifier.spage159en_US
dc.identifier.epage166en_US
dc.identifier.isiWOS:000281982000008-
dc.publisher.placeNetherlandsen_US
dc.identifier.scopusauthoridDong, J=9039009000en_US
dc.identifier.scopusauthoridCheung, KC=10038874000en_US
dc.identifier.scopusauthoridYang, H=7406559537en_US
dc.identifier.citeulike7377669-

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