Ruin and dividend measures in the renewal dual risk model
Autor(a) principal: | |
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Data de Publicação: | 2021 |
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/10400.5/24439 |
Resumo: | In this manuscript we consider the dual risk model with financial application, where the random gains occur under a renewal process. We particularly work the Erlang(n) case for common distribution of the inter-arrival times, from there it is easy to understand that our method or procedures can be generalised to other cases under the matrix-exponential family case. We work several and different problems involving future dividends and ruin. We also show that our results are valid even if the usual income condition is not satisfied. In most known works under the dual model, the main target under study have been the calculation of expected discounted future dividends and optimal strategies, where the dividend calculation have been done on aggregate. We can find works, at first using the classical compound Poisson model, then some examples of other renewal Erlang models. Knowing that ruin is ultimately achieved, we find important that dividends should be evaluated on an individual basis, where the early dividend contribution for the aggregate are of utmost importance. From our calculations we can really see how much important is the contribution of the first dividend. Afonso et al. (Insur Math Econ, 53(3), 906–918, 2013) had worked similar problems for the classical compound Poisson dual model. Besides that we find explicit formulae for both the probability of getting a dividend and the distribution of the amount of a single dividend. We still work the probability distribution of the number of gains to reach a given upper target (like a constant dividend barrier) as well as for the number of gains down to ruin. We complete the study working some illustrative numerical examples that show final numbers for the several problems under study. |
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Ruin and dividend measures in the renewal dual risk modelDual Risk ModelRuin ProbabilityExpected Discounted DividendsSingle Dividend AmountDividend ProbabilityNumber of GainsIn this manuscript we consider the dual risk model with financial application, where the random gains occur under a renewal process. We particularly work the Erlang(n) case for common distribution of the inter-arrival times, from there it is easy to understand that our method or procedures can be generalised to other cases under the matrix-exponential family case. We work several and different problems involving future dividends and ruin. We also show that our results are valid even if the usual income condition is not satisfied. In most known works under the dual model, the main target under study have been the calculation of expected discounted future dividends and optimal strategies, where the dividend calculation have been done on aggregate. We can find works, at first using the classical compound Poisson model, then some examples of other renewal Erlang models. Knowing that ruin is ultimately achieved, we find important that dividends should be evaluated on an individual basis, where the early dividend contribution for the aggregate are of utmost importance. From our calculations we can really see how much important is the contribution of the first dividend. Afonso et al. (Insur Math Econ, 53(3), 906–918, 2013) had worked similar problems for the classical compound Poisson dual model. Besides that we find explicit formulae for both the probability of getting a dividend and the distribution of the amount of a single dividend. We still work the probability distribution of the number of gains to reach a given upper target (like a constant dividend barrier) as well as for the number of gains down to ruin. We complete the study working some illustrative numerical examples that show final numbers for the several problems under study.SpringerRepositório da Universidade de LisboaAlcoforado, Renata G.Bergel, Agnieszka I.Cardoso, Rui M. R.Reis, Alfredo D. Egídio dosRodríguez-Martínez, Eugenio V.2022-05-31T16:01:52Z20212021-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/24439engAlcoforado, Renata G. … [et al.] .(2021) "Ruin and dividend measures in the renewal dual risk model". Methodology and Computing in Applied Probability: pp.1-33.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:10400.5/24439Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:08:29.215951Repositório 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 |
Ruin and dividend measures in the renewal dual risk model |
title |
Ruin and dividend measures in the renewal dual risk model |
spellingShingle |
Ruin and dividend measures in the renewal dual risk model Alcoforado, Renata G. Dual Risk Model Ruin Probability Expected Discounted Dividends Single Dividend Amount Dividend Probability Number of Gains |
title_short |
Ruin and dividend measures in the renewal dual risk model |
title_full |
Ruin and dividend measures in the renewal dual risk model |
title_fullStr |
Ruin and dividend measures in the renewal dual risk model |
title_full_unstemmed |
Ruin and dividend measures in the renewal dual risk model |
title_sort |
Ruin and dividend measures in the renewal dual risk model |
author |
Alcoforado, Renata G. |
author_facet |
Alcoforado, Renata G. Bergel, Agnieszka I. Cardoso, Rui M. R. Reis, Alfredo D. Egídio dos Rodríguez-Martínez, Eugenio V. |
author_role |
author |
author2 |
Bergel, Agnieszka I. Cardoso, Rui M. R. Reis, Alfredo D. Egídio dos Rodríguez-Martínez, Eugenio V. |
author2_role |
author author author author |
dc.contributor.none.fl_str_mv |
Repositório da Universidade de Lisboa |
dc.contributor.author.fl_str_mv |
Alcoforado, Renata G. Bergel, Agnieszka I. Cardoso, Rui M. R. Reis, Alfredo D. Egídio dos Rodríguez-Martínez, Eugenio V. |
dc.subject.por.fl_str_mv |
Dual Risk Model Ruin Probability Expected Discounted Dividends Single Dividend Amount Dividend Probability Number of Gains |
topic |
Dual Risk Model Ruin Probability Expected Discounted Dividends Single Dividend Amount Dividend Probability Number of Gains |
description |
In this manuscript we consider the dual risk model with financial application, where the random gains occur under a renewal process. We particularly work the Erlang(n) case for common distribution of the inter-arrival times, from there it is easy to understand that our method or procedures can be generalised to other cases under the matrix-exponential family case. We work several and different problems involving future dividends and ruin. We also show that our results are valid even if the usual income condition is not satisfied. In most known works under the dual model, the main target under study have been the calculation of expected discounted future dividends and optimal strategies, where the dividend calculation have been done on aggregate. We can find works, at first using the classical compound Poisson model, then some examples of other renewal Erlang models. Knowing that ruin is ultimately achieved, we find important that dividends should be evaluated on an individual basis, where the early dividend contribution for the aggregate are of utmost importance. From our calculations we can really see how much important is the contribution of the first dividend. Afonso et al. (Insur Math Econ, 53(3), 906–918, 2013) had worked similar problems for the classical compound Poisson dual model. Besides that we find explicit formulae for both the probability of getting a dividend and the distribution of the amount of a single dividend. We still work the probability distribution of the number of gains to reach a given upper target (like a constant dividend barrier) as well as for the number of gains down to ruin. We complete the study working some illustrative numerical examples that show final numbers for the several problems under study. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021 2021-01-01T00:00:00Z 2022-05-31T16:01:52Z |
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/10400.5/24439 |
url |
http://hdl.handle.net/10400.5/24439 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Alcoforado, Renata G. … [et al.] .(2021) "Ruin and dividend measures in the renewal dual risk model". Methodology and Computing in Applied Probability: pp.1-33. |
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 |
Springer |
publisher.none.fl_str_mv |
Springer |
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 |
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