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Article: Ruin in the perturbed compound Poisson risk process under interest force

TitleRuin in the perturbed compound Poisson risk process under interest force
Authors
KeywordsBrownian motion
Compound Poisson risk process
Confluent hypergeometric function
Diffusion
Hamilton-Jacobi-Bellman equation
Jump diffusion process
Kummer's confluent hypergeometric equation
Ruin probability
Viscosity solution
Issue Date2005
PublisherApplied Probability Trust. The Journal's web site is located at http://www.shef.ac.uk/uni/companies/apt/ap.html
Citation
Advances In Applied Probability, 2005, v. 37 n. 3, p. 819-835 How to Cite?
AbstractIn this paper, we study ruin in a perturbed compound Poisson risk process under stochastic interest force and constant interest force. By using the technique of stochastic control, we show that the ruin probability in the perturbed risk model is always twice continuously differentiable provided that claim sizes have continuous density functions. In the perturbed risk model, ruin may be caused by a claim or by oscillation. We decompose the ruin probability into the sum of two ruin probabilities; one is the probability that ruin is caused by a claim and the other is the probability that ruin is caused by oscillation. Integrodifferential equations for these ruin probabilities are derived when the interest force is constant. When the claim sizes are exponentially distributed, explicit solutions of the ruin probabilities are derived from the integrodifferential equations. Numerical examples are given to illustrate the effects of diffusion volatility and interest force on the ruin probabilities. © Applied Probability Trust 2005.
Persistent Identifierhttp://hdl.handle.net/10722/82946
ISSN
2015 Impact Factor: 0.654
2015 SCImago Journal Rankings: 1.009
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorCai, Jen_HK
dc.contributor.authorYang, Hen_HK
dc.date.accessioned2010-09-06T08:35:12Z-
dc.date.available2010-09-06T08:35:12Z-
dc.date.issued2005en_HK
dc.identifier.citationAdvances In Applied Probability, 2005, v. 37 n. 3, p. 819-835en_HK
dc.identifier.issn0001-8678en_HK
dc.identifier.urihttp://hdl.handle.net/10722/82946-
dc.description.abstractIn this paper, we study ruin in a perturbed compound Poisson risk process under stochastic interest force and constant interest force. By using the technique of stochastic control, we show that the ruin probability in the perturbed risk model is always twice continuously differentiable provided that claim sizes have continuous density functions. In the perturbed risk model, ruin may be caused by a claim or by oscillation. We decompose the ruin probability into the sum of two ruin probabilities; one is the probability that ruin is caused by a claim and the other is the probability that ruin is caused by oscillation. Integrodifferential equations for these ruin probabilities are derived when the interest force is constant. When the claim sizes are exponentially distributed, explicit solutions of the ruin probabilities are derived from the integrodifferential equations. Numerical examples are given to illustrate the effects of diffusion volatility and interest force on the ruin probabilities. © Applied Probability Trust 2005.en_HK
dc.languageengen_HK
dc.publisherApplied Probability Trust. The Journal's web site is located at http://www.shef.ac.uk/uni/companies/apt/ap.htmlen_HK
dc.relation.ispartofAdvances in Applied Probabilityen_HK
dc.subjectBrownian motionen_HK
dc.subjectCompound Poisson risk processen_HK
dc.subjectConfluent hypergeometric functionen_HK
dc.subjectDiffusionen_HK
dc.subjectHamilton-Jacobi-Bellman equationen_HK
dc.subjectJump diffusion processen_HK
dc.subjectKummer's confluent hypergeometric equationen_HK
dc.subjectRuin probabilityen_HK
dc.subjectViscosity solutionen_HK
dc.titleRuin in the perturbed compound Poisson risk process under interest forceen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0001-8678&volume=37&spage=819&epage=835&date=2005&atitle=Ruin+in++the+Perturbed+Compound+Poisson+Risk+Process++under+Interest+Forceen_HK
dc.identifier.emailYang, H: hlyang@hku.hken_HK
dc.identifier.authorityYang, H=rp00826en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1239/aap/1127483749en_HK
dc.identifier.scopuseid_2-s2.0-27144473473en_HK
dc.identifier.hkuros108395en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-27144473473&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume37en_HK
dc.identifier.issue3en_HK
dc.identifier.spage819en_HK
dc.identifier.epage835en_HK
dc.identifier.isiWOS:000232558300013-
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridCai, J=25222516300en_HK
dc.identifier.scopusauthoridYang, H=7406559537en_HK

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