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Article: On the discounted aggregate claim costs until ruin in dependent Sparre Andersen risk processes

TitleOn the discounted aggregate claim costs until ruin in dependent Sparre Andersen risk processes
Authors
Issue Date2016
PublisherTaylor & Francis Scandinavia. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/03461238.asp
Citation
Scandinavian Actuarial Journal, 2016, v. 2016 n. 1, p. 63-91 How to Cite?
AbstractIn this paper, a dependent Sparre Andersen risk process in which the joint density of the interclaim time and the resulting claim severity satisfies the factorization as in Willmot and Woo (2012) is considered. We study a generalization of the Gerber-Shiu function (i) whose penalty function further depends on the surplus level immediately after the second last claim before ruin (Cheung et al. (2010a)); and (ii) which involves the moments of the discounted aggregate claim costs until ruin. The generalized discounted density with a moment-based component proposed in Cheung (2013) plays a key role in deriving recursive defective renewal equations. We pay special attention to the case where the marginal distribution of the interclaim times is Coxian, and the required components in the recursion are obtained. A reverse type of dependency structure where the claim severities follow a combination of exponentials is also briefly discussed, and this leads to a nice explicit expression for the expected discounted aggregate claims until ruin. Our results are applied to generate some numerical examples involving (i) the covariance of the time of ruin and the discounted aggregate claims until ruin; and linebreak (ii) the expectation, variance and third central moment of the discounted aggregate claims until ruin.
Persistent Identifierhttp://hdl.handle.net/10722/200914
ISSN
2015 Impact Factor: 1.596
2015 SCImago Journal Rankings: 0.956

 

DC FieldValueLanguage
dc.contributor.authorCheung, ECK-
dc.contributor.authorWoo, JK-
dc.date.accessioned2014-08-21T07:07:08Z-
dc.date.available2014-08-21T07:07:08Z-
dc.date.issued2016-
dc.identifier.citationScandinavian Actuarial Journal, 2016, v. 2016 n. 1, p. 63-91-
dc.identifier.issn0346-1238-
dc.identifier.urihttp://hdl.handle.net/10722/200914-
dc.description.abstractIn this paper, a dependent Sparre Andersen risk process in which the joint density of the interclaim time and the resulting claim severity satisfies the factorization as in Willmot and Woo (2012) is considered. We study a generalization of the Gerber-Shiu function (i) whose penalty function further depends on the surplus level immediately after the second last claim before ruin (Cheung et al. (2010a)); and (ii) which involves the moments of the discounted aggregate claim costs until ruin. The generalized discounted density with a moment-based component proposed in Cheung (2013) plays a key role in deriving recursive defective renewal equations. We pay special attention to the case where the marginal distribution of the interclaim times is Coxian, and the required components in the recursion are obtained. A reverse type of dependency structure where the claim severities follow a combination of exponentials is also briefly discussed, and this leads to a nice explicit expression for the expected discounted aggregate claims until ruin. Our results are applied to generate some numerical examples involving (i) the covariance of the time of ruin and the discounted aggregate claims until ruin; and linebreak (ii) the expectation, variance and third central moment of the discounted aggregate claims until ruin.-
dc.languageeng-
dc.publisherTaylor & Francis Scandinavia. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/03461238.asp-
dc.relation.ispartofScandinavian Actuarial Journal-
dc.rightsThis is an Accepted Manuscript of an article published by Taylor & Francis in Scandinavian Actuarial Journal on 28 Mar 2014, available online: http://www.tandfonline.com/doi/full/10.1080/03461238.2014.900519-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.titleOn the discounted aggregate claim costs until ruin in dependent Sparre Andersen risk processes-
dc.typeArticle-
dc.identifier.emailCheung, ECK: eckc@hku.hk-
dc.identifier.emailWoo, JK: jkwoo@hku.hk-
dc.identifier.authorityCheung, ECK=rp01423-
dc.identifier.authorityWoo, JK=rp01623-
dc.description.naturepostprint-
dc.identifier.doi10.1080/03461238.2014.900519-
dc.identifier.scopuseid_2-s2.0-84897118956-
dc.identifier.hkuros232068-
dc.identifier.volume2016-
dc.identifier.issue1-
dc.identifier.spage63-
dc.identifier.epage91-
dc.publisher.placeSweden-

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