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Article: The maximum of randomly weighted sums with long tails in insurance and finance

TitleThe maximum of randomly weighted sums with long tails in insurance and finance
Authors
KeywordsAssociation
Asymptotics
Long tail
Maximum
Randomly weighted sum
Issue Date2011
PublisherTaylor & Francis Inc. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/07362994.asp
Citation
Stochastic Analysis and Applications, 2011, v. 29 n. 6, p. 1033-1044 How to Cite?
AbstractIn risk theory we often encounter stochastic models containing randomly weighted sums. In these sums, each primary real-valued random variable, interpreted as the net loss during a reference period, is associated with a nonnegative random weight, interpreted as the corresponding stochastic discount factor to the origin. Therefore, a weighted sum of m terms, denoted as S m (w), represents the stochastic present value of aggregate net losses during the first m periods. Suppose that the primary random variables are independent of each other with long-tailed distributions and are independent of the random weights. We show conditions on the random weights under which the tail probability of max 1≤m≤n S m (w)-the maximum of the first n weighted sums-is asymptotically equivalent to that of S n (w)-the last weighted sum. © 2011 Copyright Taylor and Francis Group, LLC.
Persistent Identifierhttp://hdl.handle.net/10722/143789
ISSN
2015 Impact Factor: 0.63
2015 SCImago Journal Rankings: 0.590
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorChen, Yen_US
dc.contributor.authorNg, KWen_US
dc.contributor.authorYuen, KCen_US
dc.date.accessioned2011-12-21T08:55:55Z-
dc.date.available2011-12-21T08:55:55Z-
dc.date.issued2011en_US
dc.identifier.citationStochastic Analysis and Applications, 2011, v. 29 n. 6, p. 1033-1044en_US
dc.identifier.issn0736-2994-
dc.identifier.urihttp://hdl.handle.net/10722/143789-
dc.description.abstractIn risk theory we often encounter stochastic models containing randomly weighted sums. In these sums, each primary real-valued random variable, interpreted as the net loss during a reference period, is associated with a nonnegative random weight, interpreted as the corresponding stochastic discount factor to the origin. Therefore, a weighted sum of m terms, denoted as S m (w), represents the stochastic present value of aggregate net losses during the first m periods. Suppose that the primary random variables are independent of each other with long-tailed distributions and are independent of the random weights. We show conditions on the random weights under which the tail probability of max 1≤m≤n S m (w)-the maximum of the first n weighted sums-is asymptotically equivalent to that of S n (w)-the last weighted sum. © 2011 Copyright Taylor and Francis Group, LLC.-
dc.languageengen_US
dc.publisherTaylor & Francis Inc. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/07362994.aspen_US
dc.relation.ispartofStochastic Analysis and Applicationsen_US
dc.rightsThis is an electronic version of an article published in Stochastic Analysis and Applications, 2011, v. 29 n. 6, p. 1033-1044. The article is available online at: http://www.tandfonline.com/doi/abs/10.1080/07362994.2011.610163-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectAssociation-
dc.subjectAsymptotics-
dc.subjectLong tail-
dc.subjectMaximum-
dc.subjectRandomly weighted sum-
dc.titleThe maximum of randomly weighted sums with long tails in insurance and financeen_US
dc.typeArticleen_US
dc.identifier.emailChen, Y: yiqing.chen@liv.ac.uken_US
dc.identifier.emailNg, KW: kaing@hkucc.hku.hken_US
dc.identifier.emailYuen, KC: kcyuen@hku.hk-
dc.identifier.authorityNg, KW=rp00765en_US
dc.identifier.authorityYuen, KC=rp00836en_US
dc.description.naturepostprint-
dc.identifier.doi10.1080/07362994.2011.610163-
dc.identifier.scopuseid_2-s2.0-84862939132-
dc.identifier.hkuros197978en_US
dc.identifier.volume29en_US
dc.identifier.issue6en_US
dc.identifier.spage1033en_US
dc.identifier.epage1044en_US
dc.identifier.isiWOS:000299780500006-
dc.publisher.placeUnited States-

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