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Article: Gerber–Shiu analysis with two-sided acceptable levels

TitleGerber–Shiu analysis with two-sided acceptable levels
Authors
KeywordsTruncated Gerber–Shiu function
Classical Poisson risk model
Surplus-dependent premium rate
Transition kernel
Joint distribution of maximum and minimum before ruin
Markovian arrival process
Issue Date2017
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/cam
Citation
Journal of Computational and Applied Mathematics, 2017, v. 321, p. 185-210 How to Cite?
AbstractIn this paper, insurer’s surplus process moved within upper and lower levels is analyzed. To this end, a truncated type of Gerber–Shiu function is proposed by further incorporating the minimum and the maximum surplus before ruin into the existing ones (e.g. Gerber and Shiu (1998), Cheung et al. (2010a)). A key component in our analysis of this proposed Gerber–Shiu function is the so-called transition kernel. Explicit expressions of the transition function under two different risk models are obtained. These two models are both generalizations of the classical Poisson risk model: (i) the first model provides flexibility in the net premium rate which is dependent on the surplus (such as linear or step function); and (ii) the second model assumes that claims arrive according to a Markovian arrival process (MAP). Finally, we discuss some applications of the truncated Gerber–Shiu function with numerical examples under various scenarios.
Persistent Identifierhttp://hdl.handle.net/10722/245295
ISSN
2020 Impact Factor: 2.621
2015 SCImago Journal Rankings: 1.089
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorWoo, JK-
dc.contributor.authorXu, R-
dc.contributor.authorYang, H-
dc.date.accessioned2017-09-18T02:08:06Z-
dc.date.available2017-09-18T02:08:06Z-
dc.date.issued2017-
dc.identifier.citationJournal of Computational and Applied Mathematics, 2017, v. 321, p. 185-210-
dc.identifier.issn0377-0427-
dc.identifier.urihttp://hdl.handle.net/10722/245295-
dc.description.abstractIn this paper, insurer’s surplus process moved within upper and lower levels is analyzed. To this end, a truncated type of Gerber–Shiu function is proposed by further incorporating the minimum and the maximum surplus before ruin into the existing ones (e.g. Gerber and Shiu (1998), Cheung et al. (2010a)). A key component in our analysis of this proposed Gerber–Shiu function is the so-called transition kernel. Explicit expressions of the transition function under two different risk models are obtained. These two models are both generalizations of the classical Poisson risk model: (i) the first model provides flexibility in the net premium rate which is dependent on the surplus (such as linear or step function); and (ii) the second model assumes that claims arrive according to a Markovian arrival process (MAP). Finally, we discuss some applications of the truncated Gerber–Shiu function with numerical examples under various scenarios.-
dc.languageeng-
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/cam-
dc.relation.ispartofJournal of Computational and Applied Mathematics-
dc.subjectTruncated Gerber–Shiu function-
dc.subjectClassical Poisson risk model-
dc.subjectSurplus-dependent premium rate-
dc.subjectTransition kernel-
dc.subjectJoint distribution of maximum and minimum before ruin-
dc.subjectMarkovian arrival process-
dc.titleGerber–Shiu analysis with two-sided acceptable levels-
dc.typeArticle-
dc.identifier.emailWoo, JK: jkwoo@hku.hk-
dc.identifier.emailYang, H: hlyang@hku.hk-
dc.identifier.authorityWoo, JK=rp01623-
dc.identifier.authorityYang, H=rp00826-
dc.identifier.doi10.1016/j.cam.2017.02.014-
dc.identifier.scopuseid_2-s2.0-85015342705-
dc.identifier.hkuros278175-
dc.identifier.hkuros289608-
dc.identifier.volume321-
dc.identifier.spage185-
dc.identifier.epage210-
dc.identifier.isiWOS:000400878000012-
dc.publisher.placeNetherlands-
dc.identifier.issnl0377-0427-

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