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Article: Dividend moments in the dual risk model: Exact and approximate approaches
Title | Dividend moments in the dual risk model: Exact and approximate approaches |
---|---|
Authors | |
Keywords | Barrier strategy Dividend moments Dual model Rational laplace transform Time of ruin |
Issue Date | 2008 |
Publisher | Peeters 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? |
Abstract | In 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 Identifier | http://hdl.handle.net/10722/92949 |
ISSN | 2015 Impact Factor: 0.732 2015 SCImago Journal Rankings: 0.979 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Cheung, ECK | en_HK |
dc.contributor.author | Drekic, S | en_HK |
dc.date.accessioned | 2010-09-22T05:04:48Z | - |
dc.date.available | 2010-09-22T05:04:48Z | - |
dc.date.issued | 2008 | en_HK |
dc.identifier.citation | Astin Bulletin, 2008, v. 38 n. 2, p. 399-422 | en_HK |
dc.identifier.issn | 0515-0361 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/92949 | - |
dc.description.abstract | In 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.language | eng | en_HK |
dc.publisher | Peeters Publishers. The Journal's web site is located at http://poj.peeters-leuven.be/content.php?url=journal&journal_code=AST | en_HK |
dc.relation.ispartof | ASTIN Bulletin | en_HK |
dc.subject | Barrier strategy | en_HK |
dc.subject | Dividend moments | en_HK |
dc.subject | Dual model | en_HK |
dc.subject | Rational laplace transform | en_HK |
dc.subject | Time of ruin | en_HK |
dc.title | Dividend moments in the dual risk model: Exact and approximate approaches | en_HK |
dc.type | Article | en_HK |
dc.identifier.email | Cheung, ECK: eckc@hku.hk | en_HK |
dc.identifier.authority | Cheung, ECK=rp01423 | en_HK |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.2143/AST.38.2.2033347 | en_HK |
dc.identifier.scopus | eid_2-s2.0-58049200161 | en_HK |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-58049200161&selection=ref&src=s&origin=recordpage | en_HK |
dc.identifier.volume | 38 | en_HK |
dc.identifier.issue | 2 | en_HK |
dc.identifier.spage | 399 | en_HK |
dc.identifier.epage | 422 | en_HK |
dc.identifier.eissn | 1783-1350 | - |
dc.identifier.isi | WOS:000261725400002 | - |
dc.publisher.place | Belgium | en_HK |
dc.identifier.scopusauthorid | Cheung, ECK=24461272100 | en_HK |
dc.identifier.scopusauthorid | Drekic, S=6603026913 | en_HK |