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Article: On the decomposition of the absolute ruin probability in a perturbed compound Poisson surplus process with debit interest
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TitleOn the decomposition of the absolute ruin probability in a perturbed compound Poisson surplus process with debit interest
 
AuthorsCai, J1 3
Yang, H2
 
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
 
CitationAnnals Of Operations Research, 2014, v. 212 n. 1, p. 61-77 [How to Cite?]
DOI: http://dx.doi.org/10.1007/s10479-011-1032-y
 
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.
 
ISSN0254-5330
2013 Impact Factor: 1.103
 
DOIhttp://dx.doi.org/10.1007/s10479-011-1032-y
 
DC FieldValue
dc.contributor.authorCai, J
 
dc.contributor.authorYang, H
 
dc.date.accessioned2012-10-30T06:22:46Z
 
dc.date.available2012-10-30T06:22:46Z
 
dc.date.issued2014
 
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.
 
dc.description.natureLink_to_subscribed_fulltext
 
dc.identifier.citationAnnals Of Operations Research, 2014, v. 212 n. 1, p. 61-77 [How to Cite?]
DOI: http://dx.doi.org/10.1007/s10479-011-1032-y
 
dc.identifier.citeulike10113213
 
dc.identifier.doihttp://dx.doi.org/10.1007/s10479-011-1032-y
 
dc.identifier.epage77
 
dc.identifier.hkuros229402
 
dc.identifier.issn0254-5330
2013 Impact Factor: 1.103
 
dc.identifier.scopuseid_2-s2.0-84891901564
 
dc.identifier.spage61
 
dc.identifier.urihttp://hdl.handle.net/10722/172488
 
dc.languageeng
 
dc.publisherSpringer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0254-5330
 
dc.publisher.placeUnited States
 
dc.relation.ispartofAnnals of Operations Research
 
dc.subjectAbsolute Ruin
 
dc.subjectBrownian Motion
 
dc.subjectCompound Poisson Process
 
dc.subjectConfluent Hypergeometric Function
 
dc.subjectDebit Interest
 
dc.subjectDefective Renewal Equation
 
dc.subjectItô Formula
 
dc.subjectKey Renewal Theorem
 
dc.subjectLong-Tailed Distribution
 
dc.subjectSubexponential Distribution
 
dc.titleOn the decomposition of the absolute ruin probability in a perturbed compound Poisson surplus process with debit interest
 
dc.typeArticle
 
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<contributor.author>Yang, H</contributor.author>
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Author Affiliations
  1. Central University of Finance
  2. The University of Hong Kong
  3. University of Waterloo