Fourier-Laplace transforms and ruin probabilities
Autor(a) principal: | |
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Data de Publicação: | 2002 |
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/10400.5/24472 |
Resumo: | In this paper we use Fourier/Laplace transforms to evaluate numerically relevant probabilities in ruin theory as an application to insurance. The transform of a function is split in two: the real and the imaginary parts. We use an inversion formula based on the real part only, to get the original function. By using an appropriate algorithm to compute integrals and making use of the properties of these transforms we are able to compute numerically important quantities either in classical or non-classical ruin theory. As far as the classical model is concerned the problems considered have been widely studied. In what concerns the non-classical model, in particular models based on more general renewal risk processes, there is still a long way to go. In either case the approach presented is an easy method giving good approximations for reasonable values of the initial surplus. To show this we compute numerically ruin probabilities in the classical model and in a renewal risk process in which claim inter-arrival times have an Erlang(2) distribution and compare to exact figures where available. We also consider the computation of the probability and severity of ruin in the classical model. |
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Fourier-Laplace transforms and ruin probabilitiesRisk TheoryRuin TheoryFourier TransformLaplace TransformProbability of Ultimate RuinSeverity of RuinErlang(2) Risk ProcessIn this paper we use Fourier/Laplace transforms to evaluate numerically relevant probabilities in ruin theory as an application to insurance. The transform of a function is split in two: the real and the imaginary parts. We use an inversion formula based on the real part only, to get the original function. By using an appropriate algorithm to compute integrals and making use of the properties of these transforms we are able to compute numerically important quantities either in classical or non-classical ruin theory. As far as the classical model is concerned the problems considered have been widely studied. In what concerns the non-classical model, in particular models based on more general renewal risk processes, there is still a long way to go. In either case the approach presented is an easy method giving good approximations for reasonable values of the initial surplus. To show this we compute numerically ruin probabilities in the classical model and in a renewal risk process in which claim inter-arrival times have an Erlang(2) distribution and compare to exact figures where available. We also consider the computation of the probability and severity of ruin in the classical model.Cambridge School PressRepositório da Universidade de LisboaLima, Fátima D. E.Garcia, Jorge M. A.Reis, Alfredo D. Egídio dos2022-06-02T14:04:43Z20022002-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/24472engLima, Fátima DP; Jorge MA Garcia and Alfredo D. Egídio dos Reis. (2002). "Fourier/Laplace transforms and ruin probabilities”. ASTIN Bulletin: The Journal of the IAA. Vol. 32, nº 1: pp. 91-105.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:RCAAP2023-03-06T14:54:07Zoai:www.repository.utl.pt:10400.5/24472Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:08:30.661942Repositório 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 |
Fourier-Laplace transforms and ruin probabilities |
title |
Fourier-Laplace transforms and ruin probabilities |
spellingShingle |
Fourier-Laplace transforms and ruin probabilities Lima, Fátima D. E. Risk Theory Ruin Theory Fourier Transform Laplace Transform Probability of Ultimate Ruin Severity of Ruin Erlang(2) Risk Process |
title_short |
Fourier-Laplace transforms and ruin probabilities |
title_full |
Fourier-Laplace transforms and ruin probabilities |
title_fullStr |
Fourier-Laplace transforms and ruin probabilities |
title_full_unstemmed |
Fourier-Laplace transforms and ruin probabilities |
title_sort |
Fourier-Laplace transforms and ruin probabilities |
author |
Lima, Fátima D. E. |
author_facet |
Lima, Fátima D. E. Garcia, Jorge M. A. Reis, Alfredo D. Egídio dos |
author_role |
author |
author2 |
Garcia, Jorge M. A. 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 |
Lima, Fátima D. E. Garcia, Jorge M. A. Reis, Alfredo D. Egídio dos |
dc.subject.por.fl_str_mv |
Risk Theory Ruin Theory Fourier Transform Laplace Transform Probability of Ultimate Ruin Severity of Ruin Erlang(2) Risk Process |
topic |
Risk Theory Ruin Theory Fourier Transform Laplace Transform Probability of Ultimate Ruin Severity of Ruin Erlang(2) Risk Process |
description |
In this paper we use Fourier/Laplace transforms to evaluate numerically relevant probabilities in ruin theory as an application to insurance. The transform of a function is split in two: the real and the imaginary parts. We use an inversion formula based on the real part only, to get the original function. By using an appropriate algorithm to compute integrals and making use of the properties of these transforms we are able to compute numerically important quantities either in classical or non-classical ruin theory. As far as the classical model is concerned the problems considered have been widely studied. In what concerns the non-classical model, in particular models based on more general renewal risk processes, there is still a long way to go. In either case the approach presented is an easy method giving good approximations for reasonable values of the initial surplus. To show this we compute numerically ruin probabilities in the classical model and in a renewal risk process in which claim inter-arrival times have an Erlang(2) distribution and compare to exact figures where available. We also consider the computation of the probability and severity of ruin in the classical model. |
publishDate |
2002 |
dc.date.none.fl_str_mv |
2002 2002-01-01T00:00:00Z 2022-06-02T14:04:43Z |
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/10400.5/24472 |
url |
http://hdl.handle.net/10400.5/24472 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Lima, Fátima DP; Jorge MA Garcia and Alfredo D. Egídio dos Reis. (2002). "Fourier/Laplace transforms and ruin probabilities”. ASTIN Bulletin: The Journal of the IAA. Vol. 32, nº 1: pp. 91-105. |
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 |
Cambridge School Press |
publisher.none.fl_str_mv |
Cambridge School Press |
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 |
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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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1799131179464523776 |