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

Authors  
Keywords  Classical Poisson risk model Expected total discounted capital injection Laplace transform of time to ruin Number of claims Preventive maintenance 
Issue Date  2018 
Publisher  Cambridge 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. 296325 How to Cite? 
Abstract  In 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 Identifier  http://hdl.handle.net/10722/272972 
ISSN 
DC Field  Value  Language 

dc.contributor.author  Xu, R   
dc.contributor.author  Woo, JK   
dc.contributor.author  Han, X   
dc.contributor.author  Yang, H   
dc.date.accessioned  20190806T09:20:09Z   
dc.date.available  20190806T09:20:09Z   
dc.date.issued  2018   
dc.identifier.citation  Annals of Actuarial Science, 2018, v. 12 n. 2, p. 296325   
dc.identifier.issn  17484995   
dc.identifier.uri  http://hdl.handle.net/10722/272972   
dc.description.abstract  In 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.language  eng   
dc.publisher  Cambridge University Press. The Journal's web site is located at http://journals.cambridge.org/action/displayJournal?jid=AAS   
dc.relation.ispartof  Annals of Actuarial Science   
dc.rights  Annals of Actuarial Science. Copyright © Cambridge University Press.   
dc.rights  This 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 redistribution, resale or use in derivative works. © the authors.   
dc.subject  Classical Poisson risk model   
dc.subject  Expected total discounted capital injection   
dc.subject  Laplace transform of time to ruin   
dc.subject  Number of claims   
dc.subject  Preventive maintenance   
dc.title  A plan of capital injections based on the claims frequency   
dc.type  Article   
dc.identifier.email  Yang, H: hlyang@hku.hk   
dc.identifier.authority  Yang, H=rp00826   
dc.description.nature  postprint   
dc.identifier.doi  10.1017/S1748499518000180   
dc.identifier.scopus  eid_2s2.085060936452   
dc.identifier.hkuros  299915   
dc.identifier.volume  12   
dc.identifier.issue  2   
dc.identifier.spage  296   
dc.identifier.epage  325   
dc.publisher.place  United Kingdom   