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Article: Dependent risk models with bivariate phase-type distributions

TitleDependent risk models with bivariate phase-type distributions
Authors
KeywordsBivariate phase-type distribution
Deficit at ruin
Fluid queue
Gerber-Shiu function
Surplus prior to ruin
Surplus process
Issue Date2009
PublisherApplied Probability Trust. The Journal's web site is located at http://www.shef.ac.uk/uni/companies/apt/ap.html
Citation
Journal Of Applied Probability, 2009, v. 46 n. 1, p. 113-131 How to Cite?
AbstractIn this paper we consider an extension of the Sparre Andersen insurance risk model by relaxing one of its independence assumptions. The newly proposed dependence structure is introduced through the premise that the joint distribution of the interclaim time and the subsequent claim size is bivariate phase-type (see, e.g. Assaf et al. (1984) and Kulkarni (1989)). Relying on the existing connection between risk processes and fluid flows (see, e.g. Badescu et al. (2005), Badescu, Drekic and Landriault (2007), Ramaswami (2006), and Ahn, Badescu and Ramaswami (2007)), we construct an analytically tractable fluid flow that leads to the analysis of various ruin-related quantities in the aforementioned risk model. Using matrix-analytic methods, we obtain an explicit expression for the Gerber - Shiu discounted penalty function (see Gerber and Shiu (1998)) when the penalty function depends on the deficit at ruin only. Finally, we investigate how some ruin-related quantities involving the surplus immediately prior to ruin can also be analyzed via our fluid flow methodology. © Applied Probability Trust 2009.
Persistent Identifierhttp://hdl.handle.net/10722/92951
ISSN
2015 Impact Factor: 0.665
2015 SCImago Journal Rankings: 0.742
References

 

DC FieldValueLanguage
dc.contributor.authorBadescu, ALen_HK
dc.contributor.authorCheung, ECKen_HK
dc.contributor.authorLandriault, Den_HK
dc.date.accessioned2010-09-22T05:04:52Z-
dc.date.available2010-09-22T05:04:52Z-
dc.date.issued2009en_HK
dc.identifier.citationJournal Of Applied Probability, 2009, v. 46 n. 1, p. 113-131en_HK
dc.identifier.issn0021-9002en_HK
dc.identifier.urihttp://hdl.handle.net/10722/92951-
dc.description.abstractIn this paper we consider an extension of the Sparre Andersen insurance risk model by relaxing one of its independence assumptions. The newly proposed dependence structure is introduced through the premise that the joint distribution of the interclaim time and the subsequent claim size is bivariate phase-type (see, e.g. Assaf et al. (1984) and Kulkarni (1989)). Relying on the existing connection between risk processes and fluid flows (see, e.g. Badescu et al. (2005), Badescu, Drekic and Landriault (2007), Ramaswami (2006), and Ahn, Badescu and Ramaswami (2007)), we construct an analytically tractable fluid flow that leads to the analysis of various ruin-related quantities in the aforementioned risk model. Using matrix-analytic methods, we obtain an explicit expression for the Gerber - Shiu discounted penalty function (see Gerber and Shiu (1998)) when the penalty function depends on the deficit at ruin only. Finally, we investigate how some ruin-related quantities involving the surplus immediately prior to ruin can also be analyzed via our fluid flow methodology. © Applied Probability Trust 2009.en_HK
dc.languageengen_HK
dc.publisherApplied Probability Trust. The Journal's web site is located at http://www.shef.ac.uk/uni/companies/apt/ap.htmlen_HK
dc.relation.ispartofJournal of Applied Probabilityen_HK
dc.subjectBivariate phase-type distributionen_HK
dc.subjectDeficit at ruinen_HK
dc.subjectFluid queueen_HK
dc.subjectGerber-Shiu functionen_HK
dc.subjectSurplus prior to ruinen_HK
dc.subjectSurplus processen_HK
dc.titleDependent risk models with bivariate phase-type distributionsen_HK
dc.typeArticleen_HK
dc.identifier.emailCheung, ECK: eckc@hku.hken_HK
dc.identifier.authorityCheung, ECK=rp01423en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1239/jap/1238592120en_HK
dc.identifier.scopuseid_2-s2.0-64249120249en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-64249120249&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume46en_HK
dc.identifier.issue1en_HK
dc.identifier.spage113en_HK
dc.identifier.epage131en_HK
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridBadescu, AL=16315079400en_HK
dc.identifier.scopusauthoridCheung, ECK=24461272100en_HK
dc.identifier.scopusauthoridLandriault, D=23479800100en_HK

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