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Article: On the decomposition of the absolute ruin probability in a perturbed compound Poisson surplus process with debit interest

TitleOn the decomposition of the absolute ruin probability in a perturbed compound Poisson surplus process with debit interest
Authors
KeywordsAbsolute Ruin
Brownian Motion
Compound Poisson Process
Confluent Hypergeometric Function
Debit Interest
Defective Renewal Equation
Itô Formula
Key Renewal Theorem
Long-Tailed Distribution
Subexponential Distribution
Issue Date2014
PublisherSpringer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0254-5330
Citation
Annals Of Operations Research, 2014, v. 212 n. 1, p. 61-77 How to Cite?
AbstractWe consider a compound Poisson surplus process perturbed by diffusion with debit interest. When the surplus is below zero or the company is on deficit, the company is allowed to borrow money at a debit interest rate to continue its business as long as its debt is at a reasonable level. When the surplus of a company is below a certain critical level, the company is no longer profitable, we say that absolute ruin occurs at this situation. In this risk model, absolute ruin may be caused by a claim or by oscillation. Thus, the absolute ruin probability in the model is decomposed as the sum of two absolute ruin probabilities, where one is the probability that absolute ruin is caused by a claim and the other is the probability that absolute ruin is caused by oscillation. In this paper, we first give the integro-differential equations satisfied by the absolute ruin probabilities and then derive the defective renewal equations for the absolute ruin probabilities. Using these defective renewal equations, we derive the asymptotical forms of the absolute ruin probabilities when the distributions of claim sizes are heavy-tailed and light-tailed. Finally, we derive explicit expressions for the absolute ruin probabilities when claim sizes are exponentially distributed. © 2011 Springer Science+Business Media, LLC.
Persistent Identifierhttp://hdl.handle.net/10722/172488
ISSN
2014 Impact Factor: 1.217
2014 SCImago Journal Rankings: 1.115
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorCai, Jen_US
dc.contributor.authorYang, Hen_US
dc.date.accessioned2012-10-30T06:22:46Z-
dc.date.available2012-10-30T06:22:46Z-
dc.date.issued2014en_US
dc.identifier.citationAnnals Of Operations Research, 2014, v. 212 n. 1, p. 61-77en_US
dc.identifier.issn0254-5330en_US
dc.identifier.urihttp://hdl.handle.net/10722/172488-
dc.description.abstractWe consider a compound Poisson surplus process perturbed by diffusion with debit interest. When the surplus is below zero or the company is on deficit, the company is allowed to borrow money at a debit interest rate to continue its business as long as its debt is at a reasonable level. When the surplus of a company is below a certain critical level, the company is no longer profitable, we say that absolute ruin occurs at this situation. In this risk model, absolute ruin may be caused by a claim or by oscillation. Thus, the absolute ruin probability in the model is decomposed as the sum of two absolute ruin probabilities, where one is the probability that absolute ruin is caused by a claim and the other is the probability that absolute ruin is caused by oscillation. In this paper, we first give the integro-differential equations satisfied by the absolute ruin probabilities and then derive the defective renewal equations for the absolute ruin probabilities. Using these defective renewal equations, we derive the asymptotical forms of the absolute ruin probabilities when the distributions of claim sizes are heavy-tailed and light-tailed. Finally, we derive explicit expressions for the absolute ruin probabilities when claim sizes are exponentially distributed. © 2011 Springer Science+Business Media, LLC.en_US
dc.languageengen_US
dc.publisherSpringer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0254-5330en_US
dc.relation.ispartofAnnals of Operations Researchen_US
dc.subjectAbsolute Ruinen_US
dc.subjectBrownian Motionen_US
dc.subjectCompound Poisson Processen_US
dc.subjectConfluent Hypergeometric Functionen_US
dc.subjectDebit Interesten_US
dc.subjectDefective Renewal Equationen_US
dc.subjectItô Formulaen_US
dc.subjectKey Renewal Theoremen_US
dc.subjectLong-Tailed Distributionen_US
dc.subjectSubexponential Distributionen_US
dc.titleOn the decomposition of the absolute ruin probability in a perturbed compound Poisson surplus process with debit interesten_US
dc.typeArticleen_US
dc.identifier.emailYang, H: hlyang@hku.hken_US
dc.identifier.authorityYang, H=rp00826en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1007/s10479-011-1032-yen_US
dc.identifier.scopuseid_2-s2.0-84891901564en_US
dc.identifier.hkuros229402-
dc.identifier.spage61en_US
dc.identifier.epage77en_US
dc.identifier.isiWOS:000329456700005-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridCai, J=25222516300en_US
dc.identifier.scopusauthoridYang, H=7406559537en_US
dc.identifier.citeulike10113213-

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