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Article: Explicit expressions for the ruin probabilities of erlang risk processes with pareto individual claim distributions

TitleExplicit expressions for the ruin probabilities of erlang risk processes with pareto individual claim distributions
Authors
KeywordsContour integration
Erlang process
Laplace transform
Pareto distribution
Removable singularity
Ruin probability
Issue Date2004
PublisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/10255/
Citation
Acta Mathematicae Applicatae Sinica, 2004, v. 20 n. 3, p. 495-506 How to Cite?
AbstractIn this paper we first consider a risk process in which claim inter-arrival times and the time until the first claim have an Erlang (2) distribution. An explicit solution is derived for the probability of ultimate ruin, given an initial reserve of u when the claim size follows a Pareto distribution. Follow Ramsay [8], Laplace transforms and exponential integrals are used to derive the solution, which involves a single integral of real valued functions along the positive real line, and the integrand is not of an oscillating kind. Then we show that the ultimate ruin probability can be expressed as the sum of expected values of functions of two different Gamma random variables. Finally, the results are extended to the Erlang(n) case. Numerical examples are given to illustrate the main results. © Springer-Verlag 2004.
Persistent Identifierhttp://hdl.handle.net/10722/82884
ISSN
2015 Impact Factor: 0.25
2015 SCImago Journal Rankings: 0.220
References

 

DC FieldValueLanguage
dc.contributor.authorWei, Len_HK
dc.contributor.authorYang, HLen_HK
dc.date.accessioned2010-09-06T08:34:30Z-
dc.date.available2010-09-06T08:34:30Z-
dc.date.issued2004en_HK
dc.identifier.citationActa Mathematicae Applicatae Sinica, 2004, v. 20 n. 3, p. 495-506en_HK
dc.identifier.issn0168-9673en_HK
dc.identifier.urihttp://hdl.handle.net/10722/82884-
dc.description.abstractIn this paper we first consider a risk process in which claim inter-arrival times and the time until the first claim have an Erlang (2) distribution. An explicit solution is derived for the probability of ultimate ruin, given an initial reserve of u when the claim size follows a Pareto distribution. Follow Ramsay [8], Laplace transforms and exponential integrals are used to derive the solution, which involves a single integral of real valued functions along the positive real line, and the integrand is not of an oscillating kind. Then we show that the ultimate ruin probability can be expressed as the sum of expected values of functions of two different Gamma random variables. Finally, the results are extended to the Erlang(n) case. Numerical examples are given to illustrate the main results. © Springer-Verlag 2004.en_HK
dc.languageengen_HK
dc.publisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/10255/en_HK
dc.relation.ispartofActa Mathematicae Applicatae Sinicaen_HK
dc.subjectContour integrationen_HK
dc.subjectErlang processen_HK
dc.subjectLaplace transformen_HK
dc.subjectPareto distributionen_HK
dc.subjectRemovable singularityen_HK
dc.subjectRuin probabilityen_HK
dc.titleExplicit expressions for the ruin probabilities of erlang risk processes with pareto individual claim distributionsen_HK
dc.typeArticleen_HK
dc.identifier.emailYang, HL: hlyang@hku.hken_HK
dc.identifier.authorityYang, HL=rp00826en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1007/s10255-004-0187-6en_HK
dc.identifier.scopuseid_2-s2.0-42249098719en_HK
dc.identifier.hkuros101325en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-42249098719&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume20en_HK
dc.identifier.issue3en_HK
dc.identifier.spage495en_HK
dc.identifier.epage506en_HK
dc.publisher.placeGermanyen_HK
dc.identifier.scopusauthoridWei, L=55198159300en_HK
dc.identifier.scopusauthoridYang, HL=7406559537en_HK

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