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Article: Moments of discounted dividends for a threshold strategy in the compound poisson risk model

TitleMoments of discounted dividends for a threshold strategy in the compound poisson risk model
Authors
Issue Date2008
PublisherSociety of Actuaries. The Journal's web site is located at http://www.soa.org/ccm/content/?categoryID=767033
Citation
North American Actuarial Journal, 2008, v. 12 n. 3, p. 299-318 How to Cite?
AbstractWe consider a compound Poisson risk model in which part of the premium is paid to the shareholders as dividends when the surplus exceeds a specified threshold level. In this model we are interested in computing the moments of the total discounted dividends paid until ruin occurs. However, instead of employing the traditional argument, which involves conditioning on the time and amount of the first claim, we provide an alternative probabilistic approach that makes use of the (defective) joint probability density function of the time of ruin and the deficit at ruin in a classical model without a threshold. We arrive at a general formula that allows us to evaluate the moments of the total discounted dividends recursively in terms of the lower-order moments. Assuming the claim size distribution is exponential or, more generally, a finite shape and scale mixture of Erlangs, we are able to solve for all necessary components in the general recursive formula. In addition to determining the optimal threshold level to maximize the expected value of discounted dividends, we also consider finding the optimal threshold level that minimizes the coefficient of variation of discounted dividends. We present several numerical examples that illustrate the effects of the choice of optimality criterion on quantities such as the ruin probability.
Persistent Identifierhttp://hdl.handle.net/10722/92952
ISSN
2015 SCImago Journal Rankings: 1.505
References

 

DC FieldValueLanguage
dc.contributor.authorCheung, ECKen_HK
dc.contributor.authorDickson, DCMen_HK
dc.contributor.authorDrekic, Sen_HK
dc.date.accessioned2010-09-22T05:04:54Z-
dc.date.available2010-09-22T05:04:54Z-
dc.date.issued2008en_HK
dc.identifier.citationNorth American Actuarial Journal, 2008, v. 12 n. 3, p. 299-318en_HK
dc.identifier.issn1092-0277en_HK
dc.identifier.urihttp://hdl.handle.net/10722/92952-
dc.description.abstractWe consider a compound Poisson risk model in which part of the premium is paid to the shareholders as dividends when the surplus exceeds a specified threshold level. In this model we are interested in computing the moments of the total discounted dividends paid until ruin occurs. However, instead of employing the traditional argument, which involves conditioning on the time and amount of the first claim, we provide an alternative probabilistic approach that makes use of the (defective) joint probability density function of the time of ruin and the deficit at ruin in a classical model without a threshold. We arrive at a general formula that allows us to evaluate the moments of the total discounted dividends recursively in terms of the lower-order moments. Assuming the claim size distribution is exponential or, more generally, a finite shape and scale mixture of Erlangs, we are able to solve for all necessary components in the general recursive formula. In addition to determining the optimal threshold level to maximize the expected value of discounted dividends, we also consider finding the optimal threshold level that minimizes the coefficient of variation of discounted dividends. We present several numerical examples that illustrate the effects of the choice of optimality criterion on quantities such as the ruin probability.en_HK
dc.languageengen_HK
dc.publisherSociety of Actuaries. The Journal's web site is located at http://www.soa.org/ccm/content/?categoryID=767033en_HK
dc.relation.ispartofNorth American Actuarial Journalen_HK
dc.titleMoments of discounted dividends for a threshold strategy in the compound poisson risk modelen_HK
dc.typeArticleen_HK
dc.identifier.emailCheung, ECK: eckc@hku.hken_HK
dc.identifier.authorityCheung, ECK=rp01423en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.scopuseid_2-s2.0-73649127482en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-73649127482&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume12en_HK
dc.identifier.issue3en_HK
dc.identifier.spage299en_HK
dc.identifier.epage318en_HK
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridCheung, ECK=24461272100en_HK
dc.identifier.scopusauthoridDickson, DCM=7402885322en_HK
dc.identifier.scopusauthoridDrekic, S=6603026913en_HK

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