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Article: Structural properties of Gerber-Shiu functions in dependent Sparre Andersen models

TitleStructural properties of Gerber-Shiu functions in dependent Sparre Andersen models
Authors
KeywordsCompound geometric distribution
Cramer's asymptotic ruin formula
Defective renewal equation
Esscher transform
Generalized adjustment coefficient
Ladder height
Last interclaim time
Lundberg's fundamental equation
NBU
NWU
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. 46 n. 1, p. 117-126 How to Cite?
AbstractThe structure of various Gerber-Shiu functions in Sparre Andersen models allowing for possible dependence between claim sizes and interclaim times is examined. The penalty function is assumed to depend on some or all of the surplus immediately prior to ruin, the deficit at ruin, the minimum surplus before ruin, and the surplus immediately after the second last claim before ruin. Defective joint and marginal distributions involving these quantities are derived. Many of the properties in the Sparre Andersen model without dependence are seen to hold in the present model as well. A discussion of Lundberg's fundamental equation and the generalized adjustment coefficient is given, and the connection to a defective renewal equation is considered. The usual Sparre Andersen model without dependence is also discussed, and in particular the case with exponential claim sizes is considered. © 2009 Elsevier B.V. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/92954
ISSN
2015 Impact Factor: 1.378
2015 SCImago Journal Rankings: 1.000
ISI Accession Number ID
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada
Munich Reinsurance Company
Institute for Quantitative Finance and Insurance at the University of Waterloo
Funding Information:

Support for David Landriault and Gordon E. Willmot by grants from the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged. Support from the Munich Reinsurance Company is also gratefully acknowledged by Gordon E. Willmot as is support for Eric C.K. Cheung and Jae-Kyung Woo from the Institute for Quantitative Finance and Insurance at the University of Waterloo.

References

 

DC FieldValueLanguage
dc.contributor.authorCheung, ECKen_HK
dc.contributor.authorLandriault, Den_HK
dc.contributor.authorWillmot, GEen_HK
dc.contributor.authorWoo, JKen_HK
dc.date.accessioned2010-09-22T05:04:58Z-
dc.date.available2010-09-22T05:04:58Z-
dc.date.issued2010en_HK
dc.identifier.citationInsurance: Mathematics And Economics, 2010, v. 46 n. 1, p. 117-126en_HK
dc.identifier.issn0167-6687en_HK
dc.identifier.urihttp://hdl.handle.net/10722/92954-
dc.description.abstractThe structure of various Gerber-Shiu functions in Sparre Andersen models allowing for possible dependence between claim sizes and interclaim times is examined. The penalty function is assumed to depend on some or all of the surplus immediately prior to ruin, the deficit at ruin, the minimum surplus before ruin, and the surplus immediately after the second last claim before ruin. Defective joint and marginal distributions involving these quantities are derived. Many of the properties in the Sparre Andersen model without dependence are seen to hold in the present model as well. A discussion of Lundberg's fundamental equation and the generalized adjustment coefficient is given, and the connection to a defective renewal equation is considered. The usual Sparre Andersen model without dependence is also discussed, and in particular the case with exponential claim sizes is considered. © 2009 Elsevier B.V. All rights reserved.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.subjectCompound geometric distributionen_HK
dc.subjectCramer's asymptotic ruin formulaen_HK
dc.subjectDefective renewal equationen_HK
dc.subjectEsscher transformen_HK
dc.subjectGeneralized adjustment coefficienten_HK
dc.subjectLadder heighten_HK
dc.subjectLast interclaim timeen_HK
dc.subjectLundberg's fundamental equationen_HK
dc.subjectNBUen_HK
dc.subjectNWUen_HK
dc.titleStructural properties of Gerber-Shiu functions in dependent Sparre Andersen modelsen_HK
dc.typeArticleen_HK
dc.identifier.emailCheung, ECK: eckc@hku.hken_HK
dc.identifier.emailWoo, JK: jkwoo@hku.hken_HK
dc.identifier.authorityCheung, ECK=rp01423en_HK
dc.identifier.authorityWoo, JK=rp01623en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.insmatheco.2009.05.009en_HK
dc.identifier.scopuseid_2-s2.0-74249088938en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-74249088938&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume46en_HK
dc.identifier.issue1en_HK
dc.identifier.spage117en_HK
dc.identifier.epage126en_HK
dc.identifier.eissn1873-5959-
dc.identifier.isiWOS:000274926700013-
dc.publisher.placeNetherlandsen_HK
dc.identifier.scopusauthoridCheung, ECK=24461272100en_HK
dc.identifier.scopusauthoridLandriault, D=23479800100en_HK
dc.identifier.scopusauthoridWillmot, GE=6603756372en_HK
dc.identifier.scopusauthoridWoo, JK=26642855300en_HK
dc.identifier.citeulike5331416-

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