Some optimization and decision problems in proportional reinsurance

Reinsurance is one of the tools that an insurer can use to mitigate the underwriting risk and then to control its solvency. In this paper, we focus on the proportional reinsurance arrangements and we examine several optimization and decision problems of the insurer with respect to the reinsurance st...

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Detalles Bibliográficos
Autores: Castañer, Anna, Claramunt Bielsa, M. Mercè, Mármol, Maite
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2016
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/109887
Acceso en línea:https://hdl.handle.net/2445/109887
Access Level:acceso abierto
Palabra clave:Reassegurances
Gestió del risc
Matemàtica financera
Risc (Assegurances)
Equacions diferencials
Reinsurance
Risk management
Business mathematics
Risk (Insurance)
Differential equations
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oai_identifier_str oai:diposit.ub.edu:2445/109887
network_acronym_str ES
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repository_id_str
spelling Some optimization and decision problems in proportional reinsuranceCastañer, AnnaClaramunt Bielsa, M. MercèMármol, MaiteReassegurancesGestió del riscMatemàtica financeraRisc (Assegurances)Equacions diferencialsReinsuranceRisk managementBusiness mathematicsRisk (Insurance)Differential equationsReinsurance is one of the tools that an insurer can use to mitigate the underwriting risk and then to control its solvency. In this paper, we focus on the proportional reinsurance arrangements and we examine several optimization and decision problems of the insurer with respect to the reinsurance strategy. To this end, we use as decision tools not only the probability of ruin but also the random variable deficit at ruin if ruin occurs. The discounted penalty function is employed to calculate as particular cases the probability of ruin and the moments and the distribution function of the deficit at ruin if ruin occurs. We consider the classical risk theory model assuming a Poisson process and an individual claim amount phase-type distributed, modified with a proportional reinsurance with a retention level that is not constant and depends on the level of the surplus. Depending on whether the initial surplus is below or above a threshold level, the discounted penalty function behaves differently. General expressions for this discounted penalty function are obtained, as well as interesting theoretical results and explicit expressions for phase-type 2 distribution. These results are applied in numerical examples of decision problems based on the probability of ruin and on different risk measures of the deficit at ruin if ruin occurs (the expectation, the Value at Risk and the Tail Value at Risk).ASEPUMA2016info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2445/109887Articles publicats en revistes (Matemàtica Econòmica, Financera i Actuarial)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésReproducció del document publicat a: http://www.revistarecta.com/n17.htmlRect@: Revista Electrónica de Comunicaciones y Trabajos de ASEPUMA, 2016, vol. 17, num. 1, p. 35-55cc-by-nc-nd (c) Castañer, Anna et al., 2016http://creativecommons.org/licenses/by-nc-nd/3.0/esinfo:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/1098872026-05-27T06:46:51Z
dc.title.none.fl_str_mv Some optimization and decision problems in proportional reinsurance
title Some optimization and decision problems in proportional reinsurance
spellingShingle Some optimization and decision problems in proportional reinsurance
Castañer, Anna
Reassegurances
Gestió del risc
Matemàtica financera
Risc (Assegurances)
Equacions diferencials
Reinsurance
Risk management
Business mathematics
Risk (Insurance)
Differential equations
title_short Some optimization and decision problems in proportional reinsurance
title_full Some optimization and decision problems in proportional reinsurance
title_fullStr Some optimization and decision problems in proportional reinsurance
title_full_unstemmed Some optimization and decision problems in proportional reinsurance
title_sort Some optimization and decision problems in proportional reinsurance
dc.creator.none.fl_str_mv Castañer, Anna
Claramunt Bielsa, M. Mercè
Mármol, Maite
author Castañer, Anna
author_facet Castañer, Anna
Claramunt Bielsa, M. Mercè
Mármol, Maite
author_role author
author2 Claramunt Bielsa, M. Mercè
Mármol, Maite
author2_role author
author
dc.subject.none.fl_str_mv Reassegurances
Gestió del risc
Matemàtica financera
Risc (Assegurances)
Equacions diferencials
Reinsurance
Risk management
Business mathematics
Risk (Insurance)
Differential equations
topic Reassegurances
Gestió del risc
Matemàtica financera
Risc (Assegurances)
Equacions diferencials
Reinsurance
Risk management
Business mathematics
Risk (Insurance)
Differential equations
description Reinsurance is one of the tools that an insurer can use to mitigate the underwriting risk and then to control its solvency. In this paper, we focus on the proportional reinsurance arrangements and we examine several optimization and decision problems of the insurer with respect to the reinsurance strategy. To this end, we use as decision tools not only the probability of ruin but also the random variable deficit at ruin if ruin occurs. The discounted penalty function is employed to calculate as particular cases the probability of ruin and the moments and the distribution function of the deficit at ruin if ruin occurs. We consider the classical risk theory model assuming a Poisson process and an individual claim amount phase-type distributed, modified with a proportional reinsurance with a retention level that is not constant and depends on the level of the surplus. Depending on whether the initial surplus is below or above a threshold level, the discounted penalty function behaves differently. General expressions for this discounted penalty function are obtained, as well as interesting theoretical results and explicit expressions for phase-type 2 distribution. These results are applied in numerical examples of decision problems based on the probability of ruin and on different risk measures of the deficit at ruin if ruin occurs (the expectation, the Value at Risk and the Tail Value at Risk).
publishDate 2016
dc.date.none.fl_str_mv 2016
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/109887
url https://hdl.handle.net/2445/109887
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: http://www.revistarecta.com/n17.html
Rect@: Revista Electrónica de Comunicaciones y Trabajos de ASEPUMA, 2016, vol. 17, num. 1, p. 35-55
dc.rights.none.fl_str_mv cc-by-nc-nd (c) Castañer, Anna et al., 2016
http://creativecommons.org/licenses/by-nc-nd/3.0/es
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-nc-nd (c) Castañer, Anna et al., 2016
http://creativecommons.org/licenses/by-nc-nd/3.0/es
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv ASEPUMA
publisher.none.fl_str_mv ASEPUMA
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtica Econòmica, Financera i Actuarial)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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