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Article: An elementary approach to discrete models of dividend strategies

TitleAn elementary approach to discrete models of dividend strategies
Authors
KeywordsBand strategy
Dividends-penalty identity
IM13
IM50
Lundberg equation
Optimal dividends
Penalty at ruin
Issue Date2010
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/ime
Citation
Insurance: Mathematics And Economics, 2010, v. 46 n. 1, p. 109-116 How to Cite?
AbstractThe paper studies a discrete counterpart of Gerber et al. (2006). The surplus of an insurance company (before dividends) is modeled as a time-homogeneous Markov chain with possible changes of size + 1, 0, - 1, - 2, - 3, .... If a barrier strategy is applied for paying dividends, it is shown that the dividends-penalty identity holds. The identity expresses the expected present value of a penalty at ruin in terms of the expected discounted dividends until ruin and the expected present value of the penalty at ruin if no dividends are paid. For the problem of maximizing the difference between the expected discounted dividends until ruin and the expected present value of the penalty at ruin, barrier strategies play a prominent role. In some cases an optimal dividend barrier exists. The paper discusses in detail the special case where the distribution of the change in surplus does not depend on the current surplus (so that in the absence of dividends the surplus process has independent increments). A closed-form result for zero initial surplus is given, and it is shown how the relevant quantities can be calculated recursively. Finally, it is shown how optimal dividend strategies can be determined; typically, they are band strategies. © 2009 Elsevier B.V. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/125409
ISSN
2015 Impact Factor: 1.378
2015 SCImago Journal Rankings: 1.000
ISI Accession Number ID
Funding AgencyGrant Number
Principal Financial Group Foundation
Council of the Hong Kong Special Administrative Region, ChinaHKU 754008H
Funding Information:

The authors wish to thank two anonymous referees: their comments led to several improvements in the paper. Elias Shiu gratefully acknowledges the generous support from the Principal Financial Group Foundation. Hailiang Yang would like to acknowledge the Research Grants Council of the Hong Kong Special Administrative Region, China (project No. HKU 754008H).

References
Grants

 

DC FieldValueLanguage
dc.contributor.authorGerber, HUen_HK
dc.contributor.authorShiu, ESWen_HK
dc.contributor.authorYang, Hen_HK
dc.date.accessioned2010-10-31T11:29:45Z-
dc.date.available2010-10-31T11:29:45Z-
dc.date.issued2010en_HK
dc.identifier.citationInsurance: Mathematics And Economics, 2010, v. 46 n. 1, p. 109-116en_HK
dc.identifier.issn0167-6687en_HK
dc.identifier.urihttp://hdl.handle.net/10722/125409-
dc.description.abstractThe paper studies a discrete counterpart of Gerber et al. (2006). The surplus of an insurance company (before dividends) is modeled as a time-homogeneous Markov chain with possible changes of size + 1, 0, - 1, - 2, - 3, .... If a barrier strategy is applied for paying dividends, it is shown that the dividends-penalty identity holds. The identity expresses the expected present value of a penalty at ruin in terms of the expected discounted dividends until ruin and the expected present value of the penalty at ruin if no dividends are paid. For the problem of maximizing the difference between the expected discounted dividends until ruin and the expected present value of the penalty at ruin, barrier strategies play a prominent role. In some cases an optimal dividend barrier exists. The paper discusses in detail the special case where the distribution of the change in surplus does not depend on the current surplus (so that in the absence of dividends the surplus process has independent increments). A closed-form result for zero initial surplus is given, and it is shown how the relevant quantities can be calculated recursively. Finally, it is shown how optimal dividend strategies can be determined; typically, they are band strategies. © 2009 Elsevier B.V. All rights reserved.en_HK
dc.languageengen_HK
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/imeen_HK
dc.relation.ispartofInsurance: Mathematics and Economicsen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectBand strategyen_HK
dc.subjectDividends-penalty identityen_HK
dc.subjectIM13en_HK
dc.subjectIM50en_HK
dc.subjectLundberg equationen_HK
dc.subjectOptimal dividendsen_HK
dc.subjectPenalty at ruinen_HK
dc.titleAn elementary approach to discrete models of dividend strategiesen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0167-6687&volume=46&issue=1&spage=109&epage=116&date=2010&atitle=An+elementary+approach+to+discrete+models+of+dividend+strategiesen_HK
dc.identifier.emailYang, H: hlyang@hku.hken_HK
dc.identifier.authorityYang, H=rp00826en_HK
dc.description.naturepostprint-
dc.identifier.doi10.1016/j.insmatheco.2009.09.010en_HK
dc.identifier.scopuseid_2-s2.0-74249092485en_HK
dc.identifier.hkuros173055en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-74249092485&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume46en_HK
dc.identifier.issue1en_HK
dc.identifier.spage109en_HK
dc.identifier.epage116en_HK
dc.identifier.isiWOS:000274926700012-
dc.publisher.placeNetherlandsen_HK
dc.relation.projectRisk Management of Equity-Linked Insurance Products-
dc.identifier.scopusauthoridGerber, HU=7202185517en_HK
dc.identifier.scopusauthoridShiu, ESW=6603568601en_HK
dc.identifier.scopusauthoridYang, H=7406559537en_HK
dc.identifier.citeulike5877708-

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