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Article: A direct approach to the discounted penalty function

TitleA direct approach to the discounted penalty function
Authors
Issue Date2010
PublisherSociety of Actuaries. The Journal's web site is located at http://www.soa.org/ccm/content/?categoryID=767033
Citation
North American Actuarial Journal, 2010, v. 14 n. 4, p. 420-434 How to Cite?
AbstractThis paper provides a new and accessible approach to establishing certain results concerning the discounted penalty function. The direct approach consists of two steps. In the first step, closedform expressions are obtained in the special case in which the claim amount distribution is a combination of exponential distributions. A rational function is useful in this context. For the second step, one observes that the family of combinations of exponential distributions is dense. Hence, it suffices to reformulate the results of the first step to obtain general results. The surplus process has downward and upward jumps, modeled by two independent compound Poisson processes. If the distribution of the upward jumps is exponential, a series of new results can be obtained with ease. Subsequently, certain results of Gerber and Shiu [H. U. Gerber and E. S. W. Shiu, North American Actuarial Journal 2(1): 48-78 (1998)] can be reproduced. The two-step approach is also applied when an independent Wiener process is added to the surplus process. Certain results are related to Zhang et al. [Z. Zhang, H. Yang, and S. Li, Journal of Computational and Applied Mathematics 233: 1773-1784 (2010)], which uses different methods.
Persistent Identifierhttp://hdl.handle.net/10722/135503
ISSN
2015 SCImago Journal Rankings: 1.505
References

 

DC FieldValueLanguage
dc.contributor.authorAlbrecher, Hen_HK
dc.contributor.authorGerber, HUen_HK
dc.contributor.authorYang, Hen_HK
dc.date.accessioned2011-07-27T01:36:09Z-
dc.date.available2011-07-27T01:36:09Z-
dc.date.issued2010en_HK
dc.identifier.citationNorth American Actuarial Journal, 2010, v. 14 n. 4, p. 420-434en_HK
dc.identifier.issn1092-0277en_HK
dc.identifier.urihttp://hdl.handle.net/10722/135503-
dc.description.abstractThis paper provides a new and accessible approach to establishing certain results concerning the discounted penalty function. The direct approach consists of two steps. In the first step, closedform expressions are obtained in the special case in which the claim amount distribution is a combination of exponential distributions. A rational function is useful in this context. For the second step, one observes that the family of combinations of exponential distributions is dense. Hence, it suffices to reformulate the results of the first step to obtain general results. The surplus process has downward and upward jumps, modeled by two independent compound Poisson processes. If the distribution of the upward jumps is exponential, a series of new results can be obtained with ease. Subsequently, certain results of Gerber and Shiu [H. U. Gerber and E. S. W. Shiu, North American Actuarial Journal 2(1): 48-78 (1998)] can be reproduced. The two-step approach is also applied when an independent Wiener process is added to the surplus process. Certain results are related to Zhang et al. [Z. Zhang, H. Yang, and S. Li, Journal of Computational and Applied Mathematics 233: 1773-1784 (2010)], which uses different methods.en_HK
dc.languageengen_US
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.titleA direct approach to the discounted penalty functionen_HK
dc.typeArticleen_HK
dc.identifier.emailYang, H: hlyang@hku.hken_HK
dc.identifier.authorityYang, H=rp00826en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.scopuseid_2-s2.0-79954542362en_HK
dc.identifier.hkuros187189en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-79954542362&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume14en_HK
dc.identifier.issue4en_HK
dc.identifier.spage420en_HK
dc.identifier.epage434en_HK
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridAlbrecher, H=6602776321en_HK
dc.identifier.scopusauthoridGerber, HU=7202185517en_HK
dc.identifier.scopusauthoridYang, H=7406559537en_HK

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