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Article: Lundberg-type bounds for the joint distribution of surplus immediately before and at ruin under the sparre andersen model

TitleLundberg-type bounds for the joint distribution of surplus immediately before and at ruin under the sparre andersen model
Authors
Issue Date2005
PublisherSociety of Actuaries. The Journal's web site is located at http://www.soa.org/ccm/content/?categoryID=767033
Citation
North American Actuarial Journal, 2005, v. 9 n. 2, p. 85-107 How to Cite?
AbstractIn this paper we consider the Sparre Andersen insurance risk model. Three cases are discussed: the ordinary renewal risk process, stationary renewal risk process, and s-delayed renewal risk process. In the first part of the paper we study the joint distribution of surplus immediately before and at ruin under the renewal insurance risk model. By constructing an exponential martingale, we obtain Lundberg-type upper bounds for the joint distribution. Consequently we obtain bounds for the distribution of the deficit at ruin and ruin probability. In the second part of the paper, we consider the special case of phase-type claims and rederive the closed-form expression for the distribution of the severity of ruin, obtained by Drekic et al. (2003, 2004). Finally, we present some numerical results to illustrate the tightness of the bounds obtained in this paper.
Persistent Identifierhttp://hdl.handle.net/10722/82809
ISSN
2015 SCImago Journal Rankings: 1.505
References

 

DC FieldValueLanguage
dc.contributor.authorNg, ACYen_HK
dc.contributor.authorYang, Hen_HK
dc.date.accessioned2010-09-06T08:33:40Z-
dc.date.available2010-09-06T08:33:40Z-
dc.date.issued2005en_HK
dc.identifier.citationNorth American Actuarial Journal, 2005, v. 9 n. 2, p. 85-107en_HK
dc.identifier.issn1092-0277en_HK
dc.identifier.urihttp://hdl.handle.net/10722/82809-
dc.description.abstractIn this paper we consider the Sparre Andersen insurance risk model. Three cases are discussed: the ordinary renewal risk process, stationary renewal risk process, and s-delayed renewal risk process. In the first part of the paper we study the joint distribution of surplus immediately before and at ruin under the renewal insurance risk model. By constructing an exponential martingale, we obtain Lundberg-type upper bounds for the joint distribution. Consequently we obtain bounds for the distribution of the deficit at ruin and ruin probability. In the second part of the paper, we consider the special case of phase-type claims and rederive the closed-form expression for the distribution of the severity of ruin, obtained by Drekic et al. (2003, 2004). Finally, we present some numerical results to illustrate the tightness of the bounds obtained in this paper.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.titleLundberg-type bounds for the joint distribution of surplus immediately before and at ruin under the sparre andersen modelen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1092-0277&volume=9&issue=2&spage=85&epage=107&date=2005&atitle=Lundberg-type+bounds+for+the+joint+distribution+of+surplus+immediately+before+and+at+ruin+under+the+sparre+andersen+modelen_HK
dc.identifier.emailYang, H: hlyang@hku.hken_HK
dc.identifier.authorityYang, H=rp00826en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.scopuseid_2-s2.0-38649142963en_HK
dc.identifier.hkuros101334en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-38649142963&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume9en_HK
dc.identifier.issue2en_HK
dc.identifier.spage85en_HK
dc.identifier.epage107en_HK
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridNg, ACY=25930496400en_HK
dc.identifier.scopusauthoridYang, H=7406559537en_HK

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