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Article: A plan of capital injections based on the claims frequency

TitleA plan of capital injections based on the claims frequency
Authors
KeywordsClassical Poisson risk model
Expected total discounted capital injection
Laplace transform of time to ruin
Number of claims
Preventive maintenance
Issue Date2018
PublisherCambridge University Press. The Journal's web site is located at http://journals.cambridge.org/action/displayJournal?jid=AAS
Citation
Annals of Actuarial Science, 2018, v. 12 n. 2, p. 296-325 How to Cite?
AbstractIn this work, we propose a capital injection strategy which is periodically implemented based on the number of claims in the classical Poisson risk model. Especially, capital injection decisions are made at a predetermined accumulated number of claim instants, if the surplus is lower than a minimum required level. There appears to be a similar problem found in reliability theory such that preventive maintenance policies are performed at certain shock numbers. Assuming a combination of exponentials for the claim severities, we first derive an explicit expression for the discounted density of the surplus level after a certain number of claims if ruin has not yet occurred. Utilising this result, we study the expected total discounted capital injection until the first ruin time. To solve the differential equation associated with this quantity, we analyse an extended Lundberg’s fundamental equation. Similarly, an expression for the Laplace transform of the time to ruin is also explicitly found. Finally, we illustrate the applicability of the present capital injection strategy and methodologies through various numerical examples. In particular, for exponential claim severities, some optimal capital injection strategy which minimises the expected capital spending per unit time is numerically studied.
Persistent Identifierhttp://hdl.handle.net/10722/272972
ISSN

 

DC FieldValueLanguage
dc.contributor.authorXu, R-
dc.contributor.authorWoo, JK-
dc.contributor.authorHan, X-
dc.contributor.authorYang, H-
dc.date.accessioned2019-08-06T09:20:09Z-
dc.date.available2019-08-06T09:20:09Z-
dc.date.issued2018-
dc.identifier.citationAnnals of Actuarial Science, 2018, v. 12 n. 2, p. 296-325-
dc.identifier.issn1748-4995-
dc.identifier.urihttp://hdl.handle.net/10722/272972-
dc.description.abstractIn this work, we propose a capital injection strategy which is periodically implemented based on the number of claims in the classical Poisson risk model. Especially, capital injection decisions are made at a predetermined accumulated number of claim instants, if the surplus is lower than a minimum required level. There appears to be a similar problem found in reliability theory such that preventive maintenance policies are performed at certain shock numbers. Assuming a combination of exponentials for the claim severities, we first derive an explicit expression for the discounted density of the surplus level after a certain number of claims if ruin has not yet occurred. Utilising this result, we study the expected total discounted capital injection until the first ruin time. To solve the differential equation associated with this quantity, we analyse an extended Lundberg’s fundamental equation. Similarly, an expression for the Laplace transform of the time to ruin is also explicitly found. Finally, we illustrate the applicability of the present capital injection strategy and methodologies through various numerical examples. In particular, for exponential claim severities, some optimal capital injection strategy which minimises the expected capital spending per unit time is numerically studied.-
dc.languageeng-
dc.publisherCambridge University Press. The Journal's web site is located at http://journals.cambridge.org/action/displayJournal?jid=AAS-
dc.relation.ispartofAnnals of Actuarial Science-
dc.rightsAnnals of Actuarial Science. Copyright © Cambridge University Press.-
dc.rightsThis article has been published in a revised form in Annals of Actuarial Science [http://doi.org/10.1017/S1748499518000180]. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © the authors.-
dc.subjectClassical Poisson risk model-
dc.subjectExpected total discounted capital injection-
dc.subjectLaplace transform of time to ruin-
dc.subjectNumber of claims-
dc.subjectPreventive maintenance-
dc.titleA plan of capital injections based on the claims frequency-
dc.typeArticle-
dc.identifier.emailYang, H: hlyang@hku.hk-
dc.identifier.authorityYang, H=rp00826-
dc.description.naturepostprint-
dc.identifier.doi10.1017/S1748499518000180-
dc.identifier.scopuseid_2-s2.0-85060936452-
dc.identifier.hkuros299915-
dc.identifier.volume12-
dc.identifier.issue2-
dc.identifier.spage296-
dc.identifier.epage325-
dc.publisher.placeUnited Kingdom-

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