Dividend problems in the dual risk model
Autor(a) principal: | |
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Data de Publicação: | 2013 |
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/10400.5/24466 |
Resumo: | We consider the compound Poisson dual risk model, dual to the well known classical risk model for insurance applications, where premiums are regarded as costs and claims are viewed as profits. The surplus can be interpreted as a venture capital like the capital of an economic activity involved in research and development. Like most authors, we consider an upper dividend barrier so that we model the gains of the capital and its return to the capital holders. By establishing a proper and crucial connection between the two models we show and explain clearly the dividends process dynamics for the dual risk model, properties for different random quantities involved as well as their relations. Using our innovative approach we derive some already known results and go further by finding several new ones. We study different ruin and dividend probabilities, such as the calculation of the probability of a dividend, distribution of the number of dividends, expected and amount of dividends as well as the time of getting a dividend. We obtain integro-differential equations for some of the above results and also Laplace transforms. From there we can get analytical results for cases where solutions and/or inversions are possible, in other cases we may only get numerical ones. We present examples under the two cases. |
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Dividend problems in the dual risk modelDual Risk ModelClassical Risk ModelRuin ProbabilitiesDividend ProbabilitiesDiscounted DividendsDividend AmountsNumber of DividendsWe consider the compound Poisson dual risk model, dual to the well known classical risk model for insurance applications, where premiums are regarded as costs and claims are viewed as profits. The surplus can be interpreted as a venture capital like the capital of an economic activity involved in research and development. Like most authors, we consider an upper dividend barrier so that we model the gains of the capital and its return to the capital holders. By establishing a proper and crucial connection between the two models we show and explain clearly the dividends process dynamics for the dual risk model, properties for different random quantities involved as well as their relations. Using our innovative approach we derive some already known results and go further by finding several new ones. We study different ruin and dividend probabilities, such as the calculation of the probability of a dividend, distribution of the number of dividends, expected and amount of dividends as well as the time of getting a dividend. We obtain integro-differential equations for some of the above results and also Laplace transforms. From there we can get analytical results for cases where solutions and/or inversions are possible, in other cases we may only get numerical ones. We present examples under the two cases.Elsevier B.V.Repositório da Universidade de LisboaAfonso, Lourdes B.Cardoso, Rui M.RReis, Alfredo D. Egídio dos2022-06-02T09:06:32Z20132013-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/24466engAfonso, Lourdes B., Rui MR Cardoso and Alfredo D. Egídio Dos Reis. (2013) "Dividend problems in the dual risk model". Insurance: Mathematics and Economics 53 (3): pp. 906-918.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:RCAAP2023-03-06T14:54:06Zoai:www.repository.utl.pt:10400.5/24466Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:08:30.368872Repositório 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 |
Dividend problems in the dual risk model |
title |
Dividend problems in the dual risk model |
spellingShingle |
Dividend problems in the dual risk model Afonso, Lourdes B. Dual Risk Model Classical Risk Model Ruin Probabilities Dividend Probabilities Discounted Dividends Dividend Amounts Number of Dividends |
title_short |
Dividend problems in the dual risk model |
title_full |
Dividend problems in the dual risk model |
title_fullStr |
Dividend problems in the dual risk model |
title_full_unstemmed |
Dividend problems in the dual risk model |
title_sort |
Dividend problems in the dual risk model |
author |
Afonso, Lourdes B. |
author_facet |
Afonso, Lourdes B. Cardoso, Rui M.R Reis, Alfredo D. Egídio dos |
author_role |
author |
author2 |
Cardoso, Rui M.R 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 |
Afonso, Lourdes B. Cardoso, Rui M.R Reis, Alfredo D. Egídio dos |
dc.subject.por.fl_str_mv |
Dual Risk Model Classical Risk Model Ruin Probabilities Dividend Probabilities Discounted Dividends Dividend Amounts Number of Dividends |
topic |
Dual Risk Model Classical Risk Model Ruin Probabilities Dividend Probabilities Discounted Dividends Dividend Amounts Number of Dividends |
description |
We consider the compound Poisson dual risk model, dual to the well known classical risk model for insurance applications, where premiums are regarded as costs and claims are viewed as profits. The surplus can be interpreted as a venture capital like the capital of an economic activity involved in research and development. Like most authors, we consider an upper dividend barrier so that we model the gains of the capital and its return to the capital holders. By establishing a proper and crucial connection between the two models we show and explain clearly the dividends process dynamics for the dual risk model, properties for different random quantities involved as well as their relations. Using our innovative approach we derive some already known results and go further by finding several new ones. We study different ruin and dividend probabilities, such as the calculation of the probability of a dividend, distribution of the number of dividends, expected and amount of dividends as well as the time of getting a dividend. We obtain integro-differential equations for some of the above results and also Laplace transforms. From there we can get analytical results for cases where solutions and/or inversions are possible, in other cases we may only get numerical ones. We present examples under the two cases. |
publishDate |
2013 |
dc.date.none.fl_str_mv |
2013 2013-01-01T00:00:00Z 2022-06-02T09:06:32Z |
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/10400.5/24466 |
url |
http://hdl.handle.net/10400.5/24466 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Afonso, Lourdes B., Rui MR Cardoso and Alfredo D. Egídio Dos Reis. (2013) "Dividend problems in the dual risk model". Insurance: Mathematics and Economics 53 (3): pp. 906-918. |
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 |
Elsevier B.V. |
publisher.none.fl_str_mv |
Elsevier B.V. |
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) |
collection |
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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1799131179456135168 |