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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 |
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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. 296-325 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 | 2020 SCImago Journal Rankings: 0.526 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Xu, R | - |
dc.contributor.author | Woo, JK | - |
dc.contributor.author | Han, X | - |
dc.contributor.author | Yang, H | - |
dc.date.accessioned | 2019-08-06T09:20:09Z | - |
dc.date.available | 2019-08-06T09:20:09Z | - |
dc.date.issued | 2018 | - |
dc.identifier.citation | Annals of Actuarial Science, 2018, v. 12 n. 2, p. 296-325 | - |
dc.identifier.issn | 1748-4995 | - |
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 re-distribution, re-sale 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_2-s2.0-85060936452 | - |
dc.identifier.hkuros | 299915 | - |
dc.identifier.volume | 12 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 296 | - |
dc.identifier.epage | 325 | - |
dc.identifier.isi | WOS:000441448200007 | - |
dc.publisher.place | United Kingdom | - |
dc.identifier.issnl | 1748-4995 | - |