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Article: Some ruin problems for a risk process with stochastic interest

TitleSome ruin problems for a risk process with stochastic interest
Authors
Issue Date2005
PublisherSociety of Actuaries. The Journal's web site is located at http://www.soa.org/ccm/content/?categoryID=767033
Citation
North American Actuarial Journal, 2005, v. 9 n. 3, p. 129-142 How to Cite?
AbstractAs investment plays an increasingly important role in the insurance business, ruin analysis in the presence of stochastic interest (or stochastic return on investments) has become a key issue in modern risk theory, and the related results should be of interest to actuaries. Although the study of insurance risk models with stochastic interest has attracted a fair amount of attention in recent years, many significant ruin problems associated with these models remain to be investigated. In this paper we consider a risk process with stochastic interest in which the basic risk process is the classical risk process and the stochastic interest process (or the stochastic return-on-investment-generating process) is a compound Poisson process with positive drift. Within this framework, we first derive an integro-differential equation for the Gerber-Shiu expected discounted penalty function, and then obtain an exact solution to the equation. We also obtain closed-form expressions for the expected discounted penalty function in some special cases. Finally, we examine a lower bound for the ruin probability of the risk process.
Persistent Identifierhttp://hdl.handle.net/10722/172425
ISSN
2015 SCImago Journal Rankings: 1.505
References

 

DC FieldValueLanguage
dc.contributor.authorYuen, KCen_US
dc.contributor.authorWang, Gen_US
dc.date.accessioned2012-10-30T06:22:26Z-
dc.date.available2012-10-30T06:22:26Z-
dc.date.issued2005en_US
dc.identifier.citationNorth American Actuarial Journal, 2005, v. 9 n. 3, p. 129-142en_US
dc.identifier.issn1092-0277en_US
dc.identifier.urihttp://hdl.handle.net/10722/172425-
dc.description.abstractAs investment plays an increasingly important role in the insurance business, ruin analysis in the presence of stochastic interest (or stochastic return on investments) has become a key issue in modern risk theory, and the related results should be of interest to actuaries. Although the study of insurance risk models with stochastic interest has attracted a fair amount of attention in recent years, many significant ruin problems associated with these models remain to be investigated. In this paper we consider a risk process with stochastic interest in which the basic risk process is the classical risk process and the stochastic interest process (or the stochastic return-on-investment-generating process) is a compound Poisson process with positive drift. Within this framework, we first derive an integro-differential equation for the Gerber-Shiu expected discounted penalty function, and then obtain an exact solution to the equation. We also obtain closed-form expressions for the expected discounted penalty function in some special cases. Finally, we examine a lower bound for the ruin probability of the risk process.en_US
dc.languageengen_US
dc.publisherSociety of Actuaries. The Journal's web site is located at http://www.soa.org/ccm/content/?categoryID=767033en_US
dc.relation.ispartofNorth American Actuarial Journalen_US
dc.titleSome ruin problems for a risk process with stochastic interesten_US
dc.typeArticleen_US
dc.identifier.emailYuen, KC: kcyuen@hku.hken_US
dc.identifier.authorityYuen, KC=rp00836en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.scopuseid_2-s2.0-33747887395en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33747887395&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume9en_US
dc.identifier.issue3en_US
dc.identifier.spage129en_US
dc.identifier.epage142en_US
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridYuen, KC=7202333703en_US
dc.identifier.scopusauthoridWang, G=7407152599en_US

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