On dividends in the phase–type dual risk model
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.5/24443 |
Resumo: | The dual risk model assumes that the surplus of a company decreases at a constant rate over time, and grows by means of upward jumps which occur at random times with random sizes. In the present work, we study the dual risk renewal model when the waiting times are phasetype distributed. Using the roots of the fundamental and the generalized Lundberg’s equations, we get expressions for the ruin probability and the Laplace transform of the time of ruin for an arbitrary single gain distribution. Then, we address the calculation of expected discounted future dividends particularly when the individual common gains follow a phase-type distribution. We further show that the optimal dividend barrier does not depend on the initial reserve. As far as the roots of the Lundberg equations and the time of ruin are concerned, we address the existing formulae in the corresponding Sparre-Andersen insurance risk model for the first hitting time, and we generalize them to cover also the situations where we have multiple roots. We do that working a new approach and technique, approach we also use for working the dividends, unlike others, it can be also applied for every situation |
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On dividends in the phase–type dual risk modelDual Risk ModelPhase-Type DistributionLundberg’s EquationsRuin ProbabilityTime to RuinExpected Discounted DividendsThe dual risk model assumes that the surplus of a company decreases at a constant rate over time, and grows by means of upward jumps which occur at random times with random sizes. In the present work, we study the dual risk renewal model when the waiting times are phasetype distributed. Using the roots of the fundamental and the generalized Lundberg’s equations, we get expressions for the ruin probability and the Laplace transform of the time of ruin for an arbitrary single gain distribution. Then, we address the calculation of expected discounted future dividends particularly when the individual common gains follow a phase-type distribution. We further show that the optimal dividend barrier does not depend on the initial reserve. As far as the roots of the Lundberg equations and the time of ruin are concerned, we address the existing formulae in the corresponding Sparre-Andersen insurance risk model for the first hitting time, and we generalize them to cover also the situations where we have multiple roots. We do that working a new approach and technique, approach we also use for working the dividends, unlike others, it can be also applied for every situationTaylor & FrancisRepositório da Universidade de LisboaBergel, Agnieszka I.Rodríguez-Martínez, Eugenio V.Reis, Alfredo D. Egídio dos2022-05-31T19:42:20Z20172017-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/24443engBergel, Agnieszka I., Eugenio V. Rodríguez-Martínez, and Alfredo D. Egidio dos Reis. (2017). "On dividends in the phase–type dual risk model." Scandinavian Actuarial Journal. Vol. 2017, nº 9: pp. 761-784.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-03-06T14:54:05Zoai:www.repository.utl.pt:10400.5/24443Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:08:29.365390Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
On dividends in the phase–type dual risk model |
title |
On dividends in the phase–type dual risk model |
spellingShingle |
On dividends in the phase–type dual risk model Bergel, Agnieszka I. Dual Risk Model Phase-Type Distribution Lundberg’s Equations Ruin Probability Time to Ruin Expected Discounted Dividends |
title_short |
On dividends in the phase–type dual risk model |
title_full |
On dividends in the phase–type dual risk model |
title_fullStr |
On dividends in the phase–type dual risk model |
title_full_unstemmed |
On dividends in the phase–type dual risk model |
title_sort |
On dividends in the phase–type dual risk model |
author |
Bergel, Agnieszka I. |
author_facet |
Bergel, Agnieszka I. Rodríguez-Martínez, Eugenio V. Reis, Alfredo D. Egídio dos |
author_role |
author |
author2 |
Rodríguez-Martínez, Eugenio V. Reis, Alfredo D. Egídio dos |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Repositório da Universidade de Lisboa |
dc.contributor.author.fl_str_mv |
Bergel, Agnieszka I. Rodríguez-Martínez, Eugenio V. Reis, Alfredo D. Egídio dos |
dc.subject.por.fl_str_mv |
Dual Risk Model Phase-Type Distribution Lundberg’s Equations Ruin Probability Time to Ruin Expected Discounted Dividends |
topic |
Dual Risk Model Phase-Type Distribution Lundberg’s Equations Ruin Probability Time to Ruin Expected Discounted Dividends |
description |
The dual risk model assumes that the surplus of a company decreases at a constant rate over time, and grows by means of upward jumps which occur at random times with random sizes. In the present work, we study the dual risk renewal model when the waiting times are phasetype distributed. Using the roots of the fundamental and the generalized Lundberg’s equations, we get expressions for the ruin probability and the Laplace transform of the time of ruin for an arbitrary single gain distribution. Then, we address the calculation of expected discounted future dividends particularly when the individual common gains follow a phase-type distribution. We further show that the optimal dividend barrier does not depend on the initial reserve. As far as the roots of the Lundberg equations and the time of ruin are concerned, we address the existing formulae in the corresponding Sparre-Andersen insurance risk model for the first hitting time, and we generalize them to cover also the situations where we have multiple roots. We do that working a new approach and technique, approach we also use for working the dividends, unlike others, it can be also applied for every situation |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017 2017-01-01T00:00:00Z 2022-05-31T19:42:20Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.5/24443 |
url |
http://hdl.handle.net/10400.5/24443 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Bergel, Agnieszka I., Eugenio V. Rodríguez-Martínez, and Alfredo D. Egidio dos Reis. (2017). "On dividends in the phase–type dual risk model." Scandinavian Actuarial Journal. Vol. 2017, nº 9: pp. 761-784. |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Taylor & Francis |
publisher.none.fl_str_mv |
Taylor & Francis |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799131178633003008 |