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

Title | On the decomposition of the absolute ruin probability in a perturbed compound Poisson surplus process with debit interest |
---|---|

Authors | Cai, J1 3 Yang, H2 |

Keywords | Absolute 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 Date | 2014 |

Publisher | Springer 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?] DOI: http://dx.doi.org/10.1007/s10479-011-1032-y |

Abstract | We 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. |

ISSN | 0254-5330 2013 Impact Factor: 1.103 |

DOI | http://dx.doi.org/10.1007/s10479-011-1032-y |

ISI Accession Number ID | WOS:000329456700005 |

DC Field | Value |
---|---|

dc.contributor.author | Cai, J |

dc.contributor.author | Yang, H |

dc.date.accessioned | 2012-10-30T06:22:46Z |

dc.date.available | 2012-10-30T06:22:46Z |

dc.date.issued | 2014 |

dc.description.abstract | We 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.nature | link_to_subscribed_fulltext |

dc.identifier.citation | Annals 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.citeulike | 10113213 |

dc.identifier.doi | http://dx.doi.org/10.1007/s10479-011-1032-y |

dc.identifier.epage | 77 |

dc.identifier.hkuros | 229402 |

dc.identifier.isi | WOS:000329456700005 |

dc.identifier.issn | 0254-5330 2013 Impact Factor: 1.103 |

dc.identifier.scopus | eid_2-s2.0-84891901564 |

dc.identifier.spage | 61 |

dc.identifier.uri | http://hdl.handle.net/10722/172488 |

dc.language | eng |

dc.publisher | Springer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0254-5330 |

dc.publisher.place | United States |

dc.relation.ispartof | Annals of Operations Research |

dc.subject | Absolute Ruin |

dc.subject | Brownian Motion |

dc.subject | Compound Poisson Process |

dc.subject | Confluent Hypergeometric Function |

dc.subject | Debit Interest |

dc.subject | Defective Renewal Equation |

dc.subject | Itô Formula |

dc.subject | Key Renewal Theorem |

dc.subject | Long-Tailed Distribution |

dc.subject | Subexponential Distribution |

dc.title | On the decomposition of the absolute ruin probability in a perturbed compound Poisson surplus process with debit interest |

dc.type | Article |

<?xml encoding="utf-8" version="1.0"?> <item><contributor.author>Cai, J</contributor.author> <contributor.author>Yang, H</contributor.author> <date.accessioned>2012-10-30T06:22:46Z</date.accessioned> <date.available>2012-10-30T06:22:46Z</date.available> <date.issued>2014</date.issued> <identifier.citation>Annals Of Operations Research, 2014, v. 212 n. 1, p. 61-77</identifier.citation> <identifier.issn>0254-5330</identifier.issn> <identifier.uri>http://hdl.handle.net/10722/172488</identifier.uri> <description.abstract>We 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.</description.abstract> <language>eng</language> <publisher>Springer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0254-5330</publisher> <relation.ispartof>Annals of Operations Research</relation.ispartof> <subject>Absolute Ruin</subject> <subject>Brownian Motion</subject> <subject>Compound Poisson Process</subject> <subject>Confluent Hypergeometric Function</subject> <subject>Debit Interest</subject> <subject>Defective Renewal Equation</subject> <subject>Itô Formula</subject> <subject>Key Renewal Theorem</subject> <subject>Long-Tailed Distribution</subject> <subject>Subexponential Distribution</subject> <title>On the decomposition of the absolute ruin probability in a perturbed compound Poisson surplus process with debit interest</title> <type>Article</type> <description.nature>link_to_subscribed_fulltext</description.nature> <identifier.doi>10.1007/s10479-011-1032-y</identifier.doi> <identifier.scopus>eid_2-s2.0-84891901564</identifier.scopus> <identifier.hkuros>229402</identifier.hkuros> <identifier.spage>61</identifier.spage> <identifier.epage>77</identifier.epage> <identifier.isi>WOS:000329456700005</identifier.isi> <publisher.place>United States</publisher.place> <identifier.citeulike>10113213</identifier.citeulike> </item>

Author Affiliations

- Central University of Finance
- The University of Hong Kong
- University of Waterloo