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Article: A generalized penalty function with the maximum surplus prior to ruin in a MAP risk model

TitleA generalized penalty function with the maximum surplus prior to ruin in a MAP risk model
Authors
KeywordsDiscounted joint distribution
Generalized penalty function
Gerber-Shiu function
Markovian arrival process
Maximum surplus level before ruin
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. 127-134 How to Cite?
AbstractIn this paper, a risk model where claims arrive according to a Markovian arrival process (MAP) is considered. A generalization of the well-known Gerber-Shiu function is proposed by incorporating the maximum surplus level before ruin into the penalty function. For this wider class of penalty functions, we show that the generalized Gerber-Shiu function can be expressed in terms of the original Gerber-Shiu function (see e.g. [Gerber, Hans U., Shiu, Elias, S.W., 1998. On the time value of ruin. North American Actuarial Journal 2(1), 48-72]) and the Laplace transform of a first passage time which are both readily available. The generalized Gerber-Shiu function is also shown to be closely related to the original Gerber-Shiu function in the same MAP risk model subject to a dividend barrier strategy. The simplest case of a MAP risk model, namely the classical compound Poisson risk model, will be studied in more detail. In particular, the discounted joint density of the surplus prior to ruin, the deficit at ruin and the maximum surplus before ruin is obtained through analytic Laplace transform inversion of a specific generalized Gerber-Shiu function. Numerical illustrations are then examined. Crown Copyright © 2009.
Persistent Identifierhttp://hdl.handle.net/10722/92957
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
Institute for Quantitative Finance and Insurance at the University of Waterloo
Funding Information:

The authors would like to thank the. anonymous referees for their valuable comments. Support for David Landriault from grants from the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged, as is support for Eric C.K. Cheung 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.date.accessioned2010-09-22T05:05:03Z-
dc.date.available2010-09-22T05:05:03Z-
dc.date.issued2010en_HK
dc.identifier.citationInsurance: Mathematics And Economics, 2010, v. 46 n. 1, p. 127-134en_HK
dc.identifier.issn0167-6687en_HK
dc.identifier.urihttp://hdl.handle.net/10722/92957-
dc.description.abstractIn this paper, a risk model where claims arrive according to a Markovian arrival process (MAP) is considered. A generalization of the well-known Gerber-Shiu function is proposed by incorporating the maximum surplus level before ruin into the penalty function. For this wider class of penalty functions, we show that the generalized Gerber-Shiu function can be expressed in terms of the original Gerber-Shiu function (see e.g. [Gerber, Hans U., Shiu, Elias, S.W., 1998. On the time value of ruin. North American Actuarial Journal 2(1), 48-72]) and the Laplace transform of a first passage time which are both readily available. The generalized Gerber-Shiu function is also shown to be closely related to the original Gerber-Shiu function in the same MAP risk model subject to a dividend barrier strategy. The simplest case of a MAP risk model, namely the classical compound Poisson risk model, will be studied in more detail. In particular, the discounted joint density of the surplus prior to ruin, the deficit at ruin and the maximum surplus before ruin is obtained through analytic Laplace transform inversion of a specific generalized Gerber-Shiu function. Numerical illustrations are then examined. Crown Copyright © 2009.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.subjectDiscounted joint distributionen_HK
dc.subjectGeneralized penalty functionen_HK
dc.subjectGerber-Shiu functionen_HK
dc.subjectMarkovian arrival processen_HK
dc.subjectMaximum surplus level before ruinen_HK
dc.titleA generalized penalty function with the maximum surplus prior to ruin in a MAP 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.doi10.1016/j.insmatheco.2009.07.009en_HK
dc.identifier.scopuseid_2-s2.0-74249111902en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-74249111902&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume46en_HK
dc.identifier.issue1en_HK
dc.identifier.spage127en_HK
dc.identifier.epage134en_HK
dc.identifier.eissn1873-5959-
dc.identifier.isiWOS:000274926700014-
dc.publisher.placeNetherlandsen_HK
dc.identifier.scopusauthoridCheung, ECK=24461272100en_HK
dc.identifier.scopusauthoridLandriault, D=23479800100en_HK
dc.identifier.citeulike5400715-

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