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Article: On Erlang(2) risk process perturbed by diffusion

TitleOn Erlang(2) risk process perturbed by diffusion
Authors
KeywordsAdjustment-coefficient
Brownian motion with drift
Diffusion
Erlang(2) risk process
Integral equation
Lundberg's inequality
Martingale
Random walk
Issue Date2005
PublisherTaylor & Francis Inc. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/03610926.asp
Citation
Communications In Statistics - Theory And Methods, 2005, v. 34 n. 11, p. 2197-2208 How to Cite?
AbstractIn thi s article, we consider an Erlang(2) risk process perturbed by diffusion. From the extreme value distribution of Brownian motion with drift and the renewal theory, we show that the survival probability satisfies an integral equation. We then give the bounds for the ultimate ruin probability and the ruin probability caused by claim. By introducing a random walk associated with the proposed risk process, we define an adjustment-coefficient. The relation between the adjustment-coefficient and the bound is given and the Lundberg-type inequality for the bound is obtained. Also, a formula of Pollaczek-Khinchin type for the bound is derived. Using these results, the bound can be calculated when claim sizes are exponentially distributed. Copyright © Taylor & Francis, Inc.
Persistent Identifierhttp://hdl.handle.net/10722/82767
ISSN
2015 Impact Factor: 0.3
2015 SCImago Journal Rankings: 0.518
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorYuen, KCen_HK
dc.contributor.authorYang, Hen_HK
dc.contributor.authorWang, Ren_HK
dc.date.accessioned2010-09-06T08:33:11Z-
dc.date.available2010-09-06T08:33:11Z-
dc.date.issued2005en_HK
dc.identifier.citationCommunications In Statistics - Theory And Methods, 2005, v. 34 n. 11, p. 2197-2208en_HK
dc.identifier.issn0361-0926en_HK
dc.identifier.urihttp://hdl.handle.net/10722/82767-
dc.description.abstractIn thi s article, we consider an Erlang(2) risk process perturbed by diffusion. From the extreme value distribution of Brownian motion with drift and the renewal theory, we show that the survival probability satisfies an integral equation. We then give the bounds for the ultimate ruin probability and the ruin probability caused by claim. By introducing a random walk associated with the proposed risk process, we define an adjustment-coefficient. The relation between the adjustment-coefficient and the bound is given and the Lundberg-type inequality for the bound is obtained. Also, a formula of Pollaczek-Khinchin type for the bound is derived. Using these results, the bound can be calculated when claim sizes are exponentially distributed. Copyright © Taylor & Francis, Inc.en_HK
dc.languageengen_HK
dc.publisherTaylor & Francis Inc. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/03610926.aspen_HK
dc.relation.ispartofCommunications in Statistics - Theory and Methodsen_HK
dc.subjectAdjustment-coefficienten_HK
dc.subjectBrownian motion with driften_HK
dc.subjectDiffusionen_HK
dc.subjectErlang(2) risk processen_HK
dc.subjectIntegral equationen_HK
dc.subjectLundberg's inequalityen_HK
dc.subjectMartingaleen_HK
dc.subjectRandom walken_HK
dc.titleOn Erlang(2) risk process perturbed by diffusionen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0361-0926&volume=34&issue=11&spage=2197&epage=2208&date=2005&atitle=On+Erlang(2)+risk+process+perturbed+by+diffusionen_HK
dc.identifier.emailYuen, KC: kcyuen@hku.hken_HK
dc.identifier.emailYang, H: hlyang@hku.hken_HK
dc.identifier.authorityYuen, KC=rp00836en_HK
dc.identifier.authorityYang, H=rp00826en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1080/STA-200066455en_HK
dc.identifier.scopuseid_2-s2.0-27744517972en_HK
dc.identifier.hkuros115937en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-27744517972&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume34en_HK
dc.identifier.issue11en_HK
dc.identifier.spage2197en_HK
dc.identifier.epage2208en_HK
dc.identifier.isiWOS:000233019600011-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridYuen, KC=7202333703en_HK
dc.identifier.scopusauthoridYang, H=7406559537en_HK
dc.identifier.scopusauthoridWang, R=7405334582en_HK

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