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Article: Moments of discounted dividends for a threshold strategy in the compound poisson risk model
Title  Moments of discounted dividends for a threshold strategy in the compound poisson risk model 

Authors  
Issue Date  2008 
Publisher  Society of Actuaries. The Journal's web site is located at http://www.soa.org/ccm/content/?categoryID=767033 
Citation  North American Actuarial Journal, 2008, v. 12 n. 3, p. 299318 How to Cite? 
Abstract  We consider a compound Poisson risk model in which part of the premium is paid to the shareholders as dividends when the surplus exceeds a specified threshold level. In this model we are interested in computing the moments of the total discounted dividends paid until ruin occurs. However, instead of employing the traditional argument, which involves conditioning on the time and amount of the first claim, we provide an alternative probabilistic approach that makes use of the (defective) joint probability density function of the time of ruin and the deficit at ruin in a classical model without a threshold. We arrive at a general formula that allows us to evaluate the moments of the total discounted dividends recursively in terms of the lowerorder moments. Assuming the claim size distribution is exponential or, more generally, a finite shape and scale mixture of Erlangs, we are able to solve for all necessary components in the general recursive formula. In addition to determining the optimal threshold level to maximize the expected value of discounted dividends, we also consider finding the optimal threshold level that minimizes the coefficient of variation of discounted dividends. We present several numerical examples that illustrate the effects of the choice of optimality criterion on quantities such as the ruin probability. 
Persistent Identifier  http://hdl.handle.net/10722/92952 
ISSN  2015 SCImago Journal Rankings: 1.505 
References 
DC Field  Value  Language 

dc.contributor.author  Cheung, ECK  en_HK 
dc.contributor.author  Dickson, DCM  en_HK 
dc.contributor.author  Drekic, S  en_HK 
dc.date.accessioned  20100922T05:04:54Z   
dc.date.available  20100922T05:04:54Z   
dc.date.issued  2008  en_HK 
dc.identifier.citation  North American Actuarial Journal, 2008, v. 12 n. 3, p. 299318  en_HK 
dc.identifier.issn  10920277  en_HK 
dc.identifier.uri  http://hdl.handle.net/10722/92952   
dc.description.abstract  We consider a compound Poisson risk model in which part of the premium is paid to the shareholders as dividends when the surplus exceeds a specified threshold level. In this model we are interested in computing the moments of the total discounted dividends paid until ruin occurs. However, instead of employing the traditional argument, which involves conditioning on the time and amount of the first claim, we provide an alternative probabilistic approach that makes use of the (defective) joint probability density function of the time of ruin and the deficit at ruin in a classical model without a threshold. We arrive at a general formula that allows us to evaluate the moments of the total discounted dividends recursively in terms of the lowerorder moments. Assuming the claim size distribution is exponential or, more generally, a finite shape and scale mixture of Erlangs, we are able to solve for all necessary components in the general recursive formula. In addition to determining the optimal threshold level to maximize the expected value of discounted dividends, we also consider finding the optimal threshold level that minimizes the coefficient of variation of discounted dividends. We present several numerical examples that illustrate the effects of the choice of optimality criterion on quantities such as the ruin probability.  en_HK 
dc.language  eng  en_HK 
dc.publisher  Society of Actuaries. The Journal's web site is located at http://www.soa.org/ccm/content/?categoryID=767033  en_HK 
dc.relation.ispartof  North American Actuarial Journal  en_HK 
dc.title  Moments of discounted dividends for a threshold strategy in the compound poisson risk model  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.scopus  eid_2s2.073649127482  en_HK 
dc.relation.references  http://www.scopus.com/mlt/select.url?eid=2s2.073649127482&selection=ref&src=s&origin=recordpage  en_HK 
dc.identifier.volume  12  en_HK 
dc.identifier.issue  3  en_HK 
dc.identifier.spage  299  en_HK 
dc.identifier.epage  318  en_HK 
dc.publisher.place  United States  en_HK 
dc.identifier.scopusauthorid  Cheung, ECK=24461272100  en_HK 
dc.identifier.scopusauthorid  Dickson, DCM=7402885322  en_HK 
dc.identifier.scopusauthorid  Drekic, S=6603026913  en_HK 