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Article: On the absolute ruin in a MAP risk model with debit interest

TitleOn the absolute ruin in a MAP risk model with debit interest
Authors
Zhang, ZYang, HYang, H
KeywordsAbsolute ruin
Asymptotic
Discounted penalty function
Heavy-tailed distribution
MAP
Matrix renewal equation
Issue Date2011
PublisherApplied Probability Trust. The Journal's web site is located at http://www.shef.ac.uk/uni/companies/apt/ap.html
Citation
Advances In Applied Probability, 2011, v. 43 n. 1, p. 77-96 How to Cite?
DOI: http://dx.doi.org/10.1239/aap/1300198513
AbstractIn this paper we consider a risk model where claims arrive according to a Markovian arrival process (MAP). When the surplus becomes negative or the insurer is in deficit, the insurer could borrow money at a constant debit interest rate to repay the claims. We derive the integro-differential equations satisfied by the discounted penalty functions and discuss the solutions. A matrix renewal equation is obtained for the discounted penalty function provided that the initial surplus is nonnegative. Based on this matrix renewal equation, we present some asymptotic formulae for the discounted penalty functions when the claim size distributions are heavy tailed. © Applied Probability Trust 2011.
Persistent Identifierhttp://hdl.handle.net/10722/135501
ISSN
0001-8678
2021 Impact Factor: 1.060
2020 SCImago Journal Rankings: 0.690
References
References in Scopus

 

DC FieldValueLanguage
dc.contributor.authorZhang, Zen_HK
dc.contributor.authorYang, Hen_HK
dc.contributor.authorYang, Hen_HK
dc.date.accessioned2011-07-27T01:36:08Z-
dc.date.available2011-07-27T01:36:08Z-
dc.date.issued2011en_HK
dc.identifier.citationAdvances In Applied Probability, 2011, v. 43 n. 1, p. 77-96en_HK
dc.identifier.issn0001-8678en_HK
dc.identifier.urihttp://hdl.handle.net/10722/135501-
dc.description.abstractIn this paper we consider a risk model where claims arrive according to a Markovian arrival process (MAP). When the surplus becomes negative or the insurer is in deficit, the insurer could borrow money at a constant debit interest rate to repay the claims. We derive the integro-differential equations satisfied by the discounted penalty functions and discuss the solutions. A matrix renewal equation is obtained for the discounted penalty function provided that the initial surplus is nonnegative. Based on this matrix renewal equation, we present some asymptotic formulae for the discounted penalty functions when the claim size distributions are heavy tailed. © Applied Probability Trust 2011.en_HK
dc.languageengen_US
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.ispartofAdvances in Applied Probabilityen_HK
dc.rightsAdvances in Applied Probability. Copyright © Applied Probability Trust.en_US
dc.subjectAbsolute ruinen_HK
dc.subjectAsymptoticen_HK
dc.subjectDiscounted penalty functionen_HK
dc.subjectHeavy-tailed distributionen_HK
dc.subjectMAPen_HK
dc.subjectMatrix renewal equationen_HK
dc.titleOn the absolute ruin in a MAP risk model with debit interesten_HK
dc.typeArticleen_HK
dc.identifier.emailYang, H: hlyang@hku.hken_HK
dc.identifier.authorityYang, H=rp00826en_HK
dc.description.naturepostprint-
dc.identifier.doi10.1239/aap/1300198513en_HK
dc.identifier.scopuseid_2-s2.0-79953135193en_HK
dc.identifier.hkuros187181en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-79953135193&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume43en_HK
dc.identifier.issue1en_HK
dc.identifier.spage77en_HK
dc.identifier.epage96en_HK
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridZhang, Z=35219373500en_HK
dc.identifier.scopusauthoridYang, H=7406559537en_HK
dc.identifier.scopusauthoridYang, H=36078235900en_HK
dc.identifier.issnl0001-8678-

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