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Article: Characterizing a comonotonic random vector by the distribution of the sum of its components
Title | Characterizing a comonotonic random vector by the distribution of the sum of its components | ||||||
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Authors | |||||||
Keywords | Comonotonicity Convex order Distortion function Distortion risk measure Stop-loss order | ||||||
Issue Date | 2010 | ||||||
Publisher | Elsevier 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? | ||||||
Abstract | In 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 Identifier | http://hdl.handle.net/10722/125402 | ||||||
ISSN | 2015 Impact Factor: 1.378 2015 SCImago Journal Rankings: 1.000 | ||||||
ISI Accession Number ID |
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 Field | Value | Language |
---|---|---|
dc.contributor.author | Cheung, KC | en_HK |
dc.date.accessioned | 2010-10-31T11:29:22Z | - |
dc.date.available | 2010-10-31T11:29:22Z | - |
dc.date.issued | 2010 | en_HK |
dc.identifier.citation | Insurance: Mathematics And Economics, 2010, v. 47 n. 2, p. 130-136 | en_HK |
dc.identifier.issn | 0167-6687 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/125402 | - |
dc.description.abstract | In 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.language | eng | en_HK |
dc.publisher | Elsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/ime | en_HK |
dc.relation.ispartof | Insurance: Mathematics and Economics | en_HK |
dc.subject | Comonotonicity | en_HK |
dc.subject | Convex order | en_HK |
dc.subject | Distortion function | en_HK |
dc.subject | Distortion risk measure | en_HK |
dc.subject | Stop-loss order | en_HK |
dc.title | Characterizing a comonotonic random vector by the distribution of the sum of its components | en_HK |
dc.type | Article | en_HK |
dc.identifier.openurl | http://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+components | en_HK |
dc.identifier.email | Cheung, KC: kccg@hku.hk | en_HK |
dc.identifier.authority | Cheung, KC=rp00677 | en_HK |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/j.insmatheco.2010.06.004 | en_HK |
dc.identifier.scopus | eid_2-s2.0-77955655106 | en_HK |
dc.identifier.hkuros | 181905 | en_HK |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-77955655106&selection=ref&src=s&origin=recordpage | en_HK |
dc.identifier.volume | 47 | en_HK |
dc.identifier.issue | 2 | en_HK |
dc.identifier.spage | 130 | en_HK |
dc.identifier.epage | 136 | en_HK |
dc.identifier.isi | WOS:000281982000004 | - |
dc.publisher.place | Netherlands | en_HK |
dc.identifier.scopusauthorid | Cheung, KC=10038874000 | en_HK |
dc.identifier.citeulike | 7377677 | - |