Minimizing ruin probability - an optimal reinsurance problem using a dynamical setting including dependences

Detalhes bibliográficos
Autor(a) principal: Botnariuc, Adrialina
Data de Publicação: 2022
Tipo de documento: Dissertação
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.5/27174
Resumo: Mestrado Bolonha em Actuarial Science
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spelling Minimizing ruin probability - an optimal reinsurance problem using a dynamical setting including dependencesRuin probabilityExcess of lossTreatyExpected value premium principle;Dependent risksMestrado Bolonha em Actuarial ScienceReinsurance is one of the key risk management tools used by insurance companies to spread risk and receive financial protection against large losses. This comes at the price of the reinsurance premium which reduces the insurer’s profits in exchange for safety. This thesis focuses on analytically finding the optimal retention levels under three different excess of loss contracts, with the purpose of minimizing the ruin probability in infinite time and from the point of view of the insurance company. The expected value premium principle is used for the calculation of both the insurer’s and reinsurer’s premiums. The same analysis is developed when considering two dependent classes of risk. A diffusion approximation of the classical Crámer-Lundberg risk process with reinsurance is considered. After building the model, the ruin probability function is characterized and conclusions regarding the optimal strategies are drawn. For the dependent case, the optimal strategy depends not only on the marginal distributions of the underlying risk, but also on the distribution of the sum of the claim severities. To better contextualize the analytical results, a numerical analysis is developed in each case, using the R software, considering different distributions and several values for its parameters. The analytical results show that, for some particular cases of the excess of loss treaty, it is always optimum to transfer part of the risk to the reinsurer; for other cases, the optimal strategy is to retain all the risk and, for the remaining cases, it depends on the distribution of the underlying risk. The numerical results corroborate the analytical ones. In particular, the optimal reinsurance strategy under dependences is different if the two classes of risk are considered independently.Reinsurance is one of the key risk management tools used by insurance companies to spread risk and receive financial protection against large losses. This comes at the price of the reinsurance premium which reduces the insurer’s profits in exchange for safety. This thesis focuses on analytically finding the optimal retention levels under three different excess of loss contracts, with the purpose of minimizing the ruin probability in infinite time and from the point of view of the insurance company. The expected value premium principle is used for the calculation of both the insurer’s and reinsurer’s premiums. The same analysis is developed when considering two dependent classes of risk. A diffusion approximation of the classical Crámer-Lundberg risk process with reinsurance is considered. After building the model, the ruin probability function is characterized and conclusions regarding the optimal strategies are drawn. For the dependent case, the optimal strategy depends not only on the marginal distributions of the underlying risk, but also on the distribution of the sum of the claim severities. To better contextualize the analytical results, a numerical analysis is developed in each case, using the R software, considering different distributions and several values for its parameters. The analytical results show that, for some particular cases of the excess of loss treaty, it is always optimum to transfer part of the risk to the reinsurer; for other cases, the optimal strategy is to retain all the risk and, for the remaining cases, it depends on the distribution of the underlying risk. The numerical results corroborate the analytical ones. In particular, the optimal reinsurance strategy under dependences is different if the two classes of risk are considered independently.Instituto Superior de Economia e GestãoMoura, AlexandraOliveira, CarlosRepositório da Universidade de LisboaBotnariuc, Adrialina2023-02-07T19:06:11Z2022-102022-10-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisapplication/pdfhttp://hdl.handle.net/10400.5/27174engBotnariuc, Adrialina (2022). “Minimizing ruin probability - an optimal reinsurance problem using a dynamical setting including". Dissertação de Mestrado. Universidade de Lisboa. Instituto Superior de Economia e Gestão.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:RCAAP2023-03-06T14:56:34Zoai:www.repository.utl.pt:10400.5/27174Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:10:42.975686Repositório 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 Minimizing ruin probability - an optimal reinsurance problem using a dynamical setting including dependences
title Minimizing ruin probability - an optimal reinsurance problem using a dynamical setting including dependences
spellingShingle Minimizing ruin probability - an optimal reinsurance problem using a dynamical setting including dependences
Botnariuc, Adrialina
Ruin probability
Excess of lossTreaty
Expected value premium principle;
Dependent risks
title_short Minimizing ruin probability - an optimal reinsurance problem using a dynamical setting including dependences
title_full Minimizing ruin probability - an optimal reinsurance problem using a dynamical setting including dependences
title_fullStr Minimizing ruin probability - an optimal reinsurance problem using a dynamical setting including dependences
title_full_unstemmed Minimizing ruin probability - an optimal reinsurance problem using a dynamical setting including dependences
title_sort Minimizing ruin probability - an optimal reinsurance problem using a dynamical setting including dependences
author Botnariuc, Adrialina
author_facet Botnariuc, Adrialina
author_role author
dc.contributor.none.fl_str_mv Moura, Alexandra
Oliveira, Carlos
Repositório da Universidade de Lisboa
dc.contributor.author.fl_str_mv Botnariuc, Adrialina
dc.subject.por.fl_str_mv Ruin probability
Excess of lossTreaty
Expected value premium principle;
Dependent risks
topic Ruin probability
Excess of lossTreaty
Expected value premium principle;
Dependent risks
description Mestrado Bolonha em Actuarial Science
publishDate 2022
dc.date.none.fl_str_mv 2022-10
2022-10-01T00:00:00Z
2023-02-07T19:06:11Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.5/27174
url http://hdl.handle.net/10400.5/27174
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Botnariuc, Adrialina (2022). “Minimizing ruin probability - an optimal reinsurance problem using a dynamical setting including". Dissertação de Mestrado. Universidade de Lisboa. Instituto Superior de Economia e Gestão.
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 Instituto Superior de Economia e Gestão
publisher.none.fl_str_mv Instituto Superior de Economia e Gestão
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
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution 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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