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Article: Analysis of a generalized penalty function in a semi-Markovian risk model

TitleAnalysis of a generalized penalty function in a semi-Markovian risk model
Authors
Issue Date2009
PublisherSociety of Actuaries. The Journal's web site is located at http://www.soa.org/ccm/content/?categoryID=767033
Citation
North American Actuarial Journal, 2009, v. 13 n. 4, p. 497-513 How to Cite?
AbstractIn this paper an extension of the semi-Markovian risk model studied by Albrecher and Boxma (2005) is considered by allowing for general interclaim times. In such a model, we follow the ideas of Cheung et al. (2010b) and consider a generalization of the Gerber-Shiu function by incorporating two more random variables in the traditional penalty function, namely, the minimum surplus level before ruin and the surplus level immediately after the second last claim prior to ruin. It is shown that the generalized Gerber-Shiu function satisfies a matrix defective renewal equation. Detailed examples are also considered when either the interclaim times or the claim sizes are exponentially distributed. Finally, we also consider the case where the claim arrival process follows a Markovian arrival process. Probabilistic arguments are used to derive the discounted joint distribution of four random variables of interest in this risk model by capitalizing on an existing connection with a particular fluid flow process.
Persistent Identifierhttp://hdl.handle.net/10722/92948
ISSN
2015 SCImago Journal Rankings: 1.505
References

 

DC FieldValueLanguage
dc.contributor.authorCheung, ECKen_HK
dc.contributor.authorLandriault, Den_HK
dc.date.accessioned2010-09-22T05:04:47Z-
dc.date.available2010-09-22T05:04:47Z-
dc.date.issued2009en_HK
dc.identifier.citationNorth American Actuarial Journal, 2009, v. 13 n. 4, p. 497-513en_HK
dc.identifier.issn1092-0277en_HK
dc.identifier.urihttp://hdl.handle.net/10722/92948-
dc.description.abstractIn this paper an extension of the semi-Markovian risk model studied by Albrecher and Boxma (2005) is considered by allowing for general interclaim times. In such a model, we follow the ideas of Cheung et al. (2010b) and consider a generalization of the Gerber-Shiu function by incorporating two more random variables in the traditional penalty function, namely, the minimum surplus level before ruin and the surplus level immediately after the second last claim prior to ruin. It is shown that the generalized Gerber-Shiu function satisfies a matrix defective renewal equation. Detailed examples are also considered when either the interclaim times or the claim sizes are exponentially distributed. Finally, we also consider the case where the claim arrival process follows a Markovian arrival process. Probabilistic arguments are used to derive the discounted joint distribution of four random variables of interest in this risk model by capitalizing on an existing connection with a particular fluid flow process.en_HK
dc.languageengen_HK
dc.publisherSociety of Actuaries. The Journal's web site is located at http://www.soa.org/ccm/content/?categoryID=767033en_HK
dc.relation.ispartofNorth American Actuarial Journalen_HK
dc.titleAnalysis of a generalized penalty function in a semi-Markovian risk modelen_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.scopuseid_2-s2.0-74249097874en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-74249097874&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume13en_HK
dc.identifier.issue4en_HK
dc.identifier.spage497en_HK
dc.identifier.epage513en_HK
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridCheung, ECK=24461272100en_HK
dc.identifier.scopusauthoridLandriault, D=23479800100en_HK

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