How long is the surplus below zero?
Autor(a) principal: | |
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Data de Publicação: | 1993 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.5/24729 |
Resumo: | Assuming the classical compound Poisson continuous time surplus process, we consider the process as continuing if ruin occurs. Due to the assumptions presented, the surplus will go to infinity with probability one. If ruin occurs the process will temporarily stay below the zero level. The purpose of this paper is to find some features about how long the surplus will stay below zero. Using a martingale method we find the moment generating function of the duration of negative surplus, which can be multiple, as well as some moments. We also present the distribution of the number of negative surpluses. We further show that the distribution of duration time of a negative surplus is the same as the distribution of the time of ruin, given ruin occurs and initial surplus is zero. Finally, we present two examples, considering exponential and Gamma(2,β) individual claim amount distributions. |
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How long is the surplus below zero?Ruin TheoryProbability and Severity of RuinSurplus ProcessMartingalesCompound Geometric DistributionAssuming the classical compound Poisson continuous time surplus process, we consider the process as continuing if ruin occurs. Due to the assumptions presented, the surplus will go to infinity with probability one. If ruin occurs the process will temporarily stay below the zero level. The purpose of this paper is to find some features about how long the surplus will stay below zero. Using a martingale method we find the moment generating function of the duration of negative surplus, which can be multiple, as well as some moments. We also present the distribution of the number of negative surpluses. We further show that the distribution of duration time of a negative surplus is the same as the distribution of the time of ruin, given ruin occurs and initial surplus is zero. Finally, we present two examples, considering exponential and Gamma(2,β) individual claim amount distributions.ElsevierRepositório da Universidade de LisboaReis, Alfredo D. Egídio dos2022-06-30T13:38:19Z19931993-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/24729engReis, Alfredo Egídio dos .(1993). "How long is the surplus below zero?". Insurance: Mathematics and Economics, Vol. 12, No. 1 (1993): pp. 23-38.metadata only accessinfo: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:RCAAP2023-03-06T14:54:20Zoai:www.repository.utl.pt:10400.5/24729Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:08:42.556639Repositório 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 |
How long is the surplus below zero? |
title |
How long is the surplus below zero? |
spellingShingle |
How long is the surplus below zero? Reis, Alfredo D. Egídio dos Ruin Theory Probability and Severity of Ruin Surplus Process Martingales Compound Geometric Distribution |
title_short |
How long is the surplus below zero? |
title_full |
How long is the surplus below zero? |
title_fullStr |
How long is the surplus below zero? |
title_full_unstemmed |
How long is the surplus below zero? |
title_sort |
How long is the surplus below zero? |
author |
Reis, Alfredo D. Egídio dos |
author_facet |
Reis, Alfredo D. Egídio dos |
author_role |
author |
dc.contributor.none.fl_str_mv |
Repositório da Universidade de Lisboa |
dc.contributor.author.fl_str_mv |
Reis, Alfredo D. Egídio dos |
dc.subject.por.fl_str_mv |
Ruin Theory Probability and Severity of Ruin Surplus Process Martingales Compound Geometric Distribution |
topic |
Ruin Theory Probability and Severity of Ruin Surplus Process Martingales Compound Geometric Distribution |
description |
Assuming the classical compound Poisson continuous time surplus process, we consider the process as continuing if ruin occurs. Due to the assumptions presented, the surplus will go to infinity with probability one. If ruin occurs the process will temporarily stay below the zero level. The purpose of this paper is to find some features about how long the surplus will stay below zero. Using a martingale method we find the moment generating function of the duration of negative surplus, which can be multiple, as well as some moments. We also present the distribution of the number of negative surpluses. We further show that the distribution of duration time of a negative surplus is the same as the distribution of the time of ruin, given ruin occurs and initial surplus is zero. Finally, we present two examples, considering exponential and Gamma(2,β) individual claim amount distributions. |
publishDate |
1993 |
dc.date.none.fl_str_mv |
1993 1993-01-01T00:00:00Z 2022-06-30T13:38:19Z |
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/10400.5/24729 |
url |
http://hdl.handle.net/10400.5/24729 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Reis, Alfredo Egídio dos .(1993). "How long is the surplus below zero?". Insurance: Mathematics and Economics, Vol. 12, No. 1 (1993): pp. 23-38. |
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metadata only access info:eu-repo/semantics/openAccess |
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metadata only access |
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openAccess |
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application/pdf |
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Elsevier |
publisher.none.fl_str_mv |
Elsevier |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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