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Article: An elementary approach to discrete models of dividend strategies
Title | An elementary approach to discrete models of dividend strategies | ||||||
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Authors | |||||||
Keywords | Band strategy Dividends-penalty identity IM13 IM50 Lundberg equation Optimal dividends Penalty at ruin | ||||||
Issue Date | 2010 | ||||||
Publisher | Elsevier 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? | ||||||
Abstract | The 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 Identifier | http://hdl.handle.net/10722/125409 | ||||||
ISSN | 2015 Impact Factor: 1.378 2015 SCImago Journal Rankings: 1.000 | ||||||
ISI Accession Number ID |
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 Field | Value | Language |
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dc.contributor.author | Gerber, HU | en_HK |
dc.contributor.author | Shiu, ESW | en_HK |
dc.contributor.author | Yang, H | en_HK |
dc.date.accessioned | 2010-10-31T11:29:45Z | - |
dc.date.available | 2010-10-31T11:29:45Z | - |
dc.date.issued | 2010 | en_HK |
dc.identifier.citation | Insurance: Mathematics And Economics, 2010, v. 46 n. 1, p. 109-116 | en_HK |
dc.identifier.issn | 0167-6687 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/125409 | - |
dc.description.abstract | The 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.language | eng | en_HK |
dc.publisher | Elsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/ime | en_HK |
dc.relation.ispartof | Insurance: Mathematics and Economics | en_HK |
dc.rights | Creative Commons: Attribution 3.0 Hong Kong License | - |
dc.subject | Band strategy | en_HK |
dc.subject | Dividends-penalty identity | en_HK |
dc.subject | IM13 | en_HK |
dc.subject | IM50 | en_HK |
dc.subject | Lundberg equation | en_HK |
dc.subject | Optimal dividends | en_HK |
dc.subject | Penalty at ruin | en_HK |
dc.title | An elementary approach to discrete models of dividend strategies | en_HK |
dc.type | Article | en_HK |
dc.identifier.openurl | http://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+strategies | en_HK |
dc.identifier.email | Yang, H: hlyang@hku.hk | en_HK |
dc.identifier.authority | Yang, H=rp00826 | en_HK |
dc.description.nature | postprint | - |
dc.identifier.doi | 10.1016/j.insmatheco.2009.09.010 | en_HK |
dc.identifier.scopus | eid_2-s2.0-74249092485 | en_HK |
dc.identifier.hkuros | 173055 | en_HK |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-74249092485&selection=ref&src=s&origin=recordpage | en_HK |
dc.identifier.volume | 46 | en_HK |
dc.identifier.issue | 1 | en_HK |
dc.identifier.spage | 109 | en_HK |
dc.identifier.epage | 116 | en_HK |
dc.identifier.isi | WOS:000274926700012 | - |
dc.publisher.place | Netherlands | en_HK |
dc.relation.project | Risk Management of Equity-Linked Insurance Products | - |
dc.identifier.scopusauthorid | Gerber, HU=7202185517 | en_HK |
dc.identifier.scopusauthorid | Shiu, ESW=6603568601 | en_HK |
dc.identifier.scopusauthorid | Yang, H=7406559537 | en_HK |
dc.identifier.citeulike | 5877708 | - |