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Article: Dividend moments in the dual risk model: Exact and approximate approaches

TitleDividend moments in the dual risk model: Exact and approximate approaches
Authors
KeywordsBarrier strategy
Dividend moments
Dual model
Rational laplace transform
Time of ruin
Issue Date2008
PublisherPeeters Publishers. The Journal's web site is located at http://poj.peeters-leuven.be/content.php?url=journal&journal_code=AST
Citation
Astin Bulletin, 2008, v. 38 n. 2, p. 399-422 How to Cite?
AbstractIn the classical compound Poisson risk model, it is assumed that a company (typically an insurance company) receives premium at a constant rate and pays incurred claims until ruin occurs. In contrast, for certain companies (typically those focusing on invention), it might be more appropriate to assume expenses are paid at a fixed rate and occasional random income is earned. In such cases, the surplus process of the company can be modelled as a dual of the classical compound Poisson model, as described in Avanzi et al. (2007). Assuming further that a barrier strategy is applied to such a model (i.e., any overshoot beyond a fixed level caused by an upward jump is paid out as a dividend until ruin occurs), we are able to derive integro-differential equations for the moments of the total discounted dividends as well as the Laplace transform of the time of ruin. These integro-differential equations can be solved explicitly assuming the jump size distribution has a rational Laplace transform. We also propose a discrete-time analogue of the continuous-time dual model and show that the corresponding quantities can be solved for explicitly leaving the discrete jump size distribution arbitrary. While the discrete-time model can be considered as a stand-alone model, it can also serve as an approximation to the continuous-time model. Finally, we consider a generalization of the so-called Dickson-Waters modification in optimal dividends problems by maximizing the difference between the expected value of discounted dividends and the present value of a fixed penalty applied at the time of ruin. © 2008 by Astin Bulletin. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/92949
ISSN
2015 Impact Factor: 0.732
2015 SCImago Journal Rankings: 0.979
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorCheung, ECKen_HK
dc.contributor.authorDrekic, Sen_HK
dc.date.accessioned2010-09-22T05:04:48Z-
dc.date.available2010-09-22T05:04:48Z-
dc.date.issued2008en_HK
dc.identifier.citationAstin Bulletin, 2008, v. 38 n. 2, p. 399-422en_HK
dc.identifier.issn0515-0361en_HK
dc.identifier.urihttp://hdl.handle.net/10722/92949-
dc.description.abstractIn the classical compound Poisson risk model, it is assumed that a company (typically an insurance company) receives premium at a constant rate and pays incurred claims until ruin occurs. In contrast, for certain companies (typically those focusing on invention), it might be more appropriate to assume expenses are paid at a fixed rate and occasional random income is earned. In such cases, the surplus process of the company can be modelled as a dual of the classical compound Poisson model, as described in Avanzi et al. (2007). Assuming further that a barrier strategy is applied to such a model (i.e., any overshoot beyond a fixed level caused by an upward jump is paid out as a dividend until ruin occurs), we are able to derive integro-differential equations for the moments of the total discounted dividends as well as the Laplace transform of the time of ruin. These integro-differential equations can be solved explicitly assuming the jump size distribution has a rational Laplace transform. We also propose a discrete-time analogue of the continuous-time dual model and show that the corresponding quantities can be solved for explicitly leaving the discrete jump size distribution arbitrary. While the discrete-time model can be considered as a stand-alone model, it can also serve as an approximation to the continuous-time model. Finally, we consider a generalization of the so-called Dickson-Waters modification in optimal dividends problems by maximizing the difference between the expected value of discounted dividends and the present value of a fixed penalty applied at the time of ruin. © 2008 by Astin Bulletin. All rights reserved.en_HK
dc.languageengen_HK
dc.publisherPeeters Publishers. The Journal's web site is located at http://poj.peeters-leuven.be/content.php?url=journal&journal_code=ASTen_HK
dc.relation.ispartofASTIN Bulletinen_HK
dc.subjectBarrier strategyen_HK
dc.subjectDividend momentsen_HK
dc.subjectDual modelen_HK
dc.subjectRational laplace transformen_HK
dc.subjectTime of ruinen_HK
dc.titleDividend moments in the dual risk model: Exact and approximate approachesen_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.doi10.2143/AST.38.2.2033347en_HK
dc.identifier.scopuseid_2-s2.0-58049200161en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-58049200161&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume38en_HK
dc.identifier.issue2en_HK
dc.identifier.spage399en_HK
dc.identifier.epage422en_HK
dc.identifier.eissn1783-1350-
dc.identifier.isiWOS:000261725400002-
dc.publisher.placeBelgiumen_HK
dc.identifier.scopusauthoridCheung, ECK=24461272100en_HK
dc.identifier.scopusauthoridDrekic, S=6603026913en_HK

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