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Article: Surplus analysis for a class of Coxian interclaim time distributions with applications to mixed Erlang claim amounts

TitleSurplus analysis for a class of Coxian interclaim time distributions with applications to mixed Erlang claim amounts
Authors
Willmot, GEWoo, JK
KeywordsCombination of Erlangs
Compound geometric distribution
Defective renewal equation
Generalized Lundberg's fundamental equation
Kn family of distributions
Ladder height
Lagrange polynomials
Mixtures of Erlangs
Sparre Andersen risk process
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. 32-41 How to Cite?
DOI: http://dx.doi.org/10.1016/j.insmatheco.2009.08.004
AbstractGerber-Shiu analysis with the generalized penalty function proposed by Cheung et al. (in press-a) is considered in the Sparre Andersen risk model with a Kn family distribution for the interclaim time. A defective renewal equation and its solution for the present Gerber-Shiu function are derived, and their forms are natural for analysis which jointly involves the time of ruin and the surplus immediately prior to ruin. The results are then used to find explicit expressions for various defective joint and marginal densities, including those involving the claim causing ruin and the last interclaim time before ruin. The case with mixed Erlang claim amounts is considered in some detail. © 2009 Elsevier B.V. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/157714
ISSN
0167-6687
2023 Impact Factor: 1.9
2023 SCImago Journal Rankings: 1.113
ISI Accession Number ID
WOS:000274926700005
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:

The authors wish to thank both referees for their insightful comments which have undoubtedly improved the readability of the paper. Support for Gordon E. Willmot from the Natural Sciences and Engineering Research Council of Canada and the Munich Reinsurance Company is gratefully acknowleged, as is support for Jae-Kyung Woo from the Institute for Quantitative Finance and Insurance at the University of Waterloo.

References
References in Scopus

 

DC FieldValueLanguage
dc.contributor.authorWillmot, GEen_HK
dc.contributor.authorWoo, JKen_HK
dc.date.accessioned2012-08-08T08:54:23Z-
dc.date.available2012-08-08T08:54:23Z-
dc.date.issued2010en_HK
dc.identifier.citationInsurance: Mathematics And Economics, 2010, v. 46 n. 1, p. 32-41en_HK
dc.identifier.issn0167-6687en_HK
dc.identifier.urihttp://hdl.handle.net/10722/157714-
dc.description.abstractGerber-Shiu analysis with the generalized penalty function proposed by Cheung et al. (in press-a) is considered in the Sparre Andersen risk model with a Kn family distribution for the interclaim time. A defective renewal equation and its solution for the present Gerber-Shiu function are derived, and their forms are natural for analysis which jointly involves the time of ruin and the surplus immediately prior to ruin. The results are then used to find explicit expressions for various defective joint and marginal densities, including those involving the claim causing ruin and the last interclaim time before ruin. The case with mixed Erlang claim amounts is considered in some detail. © 2009 Elsevier B.V. All rights reserved.en_HK
dc.languageengen_US
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.subjectCombination of Erlangsen_HK
dc.subjectCompound geometric distributionen_HK
dc.subjectDefective renewal equationen_HK
dc.subjectGeneralized Lundberg's fundamental equationen_HK
dc.subjectKn family of distributionsen_HK
dc.subjectLadder heighten_HK
dc.subjectLagrange polynomialsen_HK
dc.subjectMixtures of Erlangsen_HK
dc.subjectSparre Andersen risk processen_HK
dc.titleSurplus analysis for a class of Coxian interclaim time distributions with applications to mixed Erlang claim amountsen_HK
dc.typeArticleen_HK
dc.identifier.emailWoo, JK: jkwoo@hku.hken_HK
dc.identifier.authorityWoo, JK=rp01623en_HK
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1016/j.insmatheco.2009.08.004en_HK
dc.identifier.scopuseid_2-s2.0-74249121472en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-74249121472&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume46en_HK
dc.identifier.issue1en_HK
dc.identifier.spage32en_HK
dc.identifier.epage41en_HK
dc.identifier.eissn1873-5959-
dc.identifier.isiWOS:000274926700005-
dc.publisher.placeNetherlandsen_HK
dc.identifier.scopusauthoridWillmot, GE=6603756372en_HK
dc.identifier.scopusauthoridWoo, JK=26642855300en_HK
dc.identifier.citeulike5707145-
dc.identifier.issnl0167-6687-

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