Publicação
Minimizing ruin probability - an optimal reinsurance problem using a dynamical setting including dependences
| Resumo: | 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.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. |
|---|---|
| Autores principais: | Botnariuc, Adrialina |
| Assunto: | Ruin probability Excess of lossTreaty Expected value premium principle; Dependent risks |
| Ano: | 2022 |
| País: | Portugal |
| Tipo de documento: | dissertação de mestrado |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório da Universidade de Lisboa |
| _version_ | 1866811094450831360 |
|---|---|
| author | Botnariuc, Adrialina |
| author_facet | Botnariuc, Adrialina |
| author_role | author |
| contributor_name_str_mv | Moura, Alexandra Oliveira, Carlos Repositório Científico de Acesso Aberto da ULisboa |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Botnariuc, Adrialina\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | Moura, Alexandra Oliveira, Carlos Repositório Científico de Acesso Aberto da ULisboa |
| datacite.creators.creator.creatorName.fl_str_mv | Botnariuc, Adrialina |
| datacite.date.Accepted.fl_str_mv | 2022-10-01T00:00:00Z |
| datacite.date.available.fl_str_mv | 2023-02-07T19:06:11Z |
| datacite.date.embargoed.fl_str_mv | 2023-02-07T19:06:11Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Ruin probability Excess of lossTreaty Expected value premium principle; Dependent risks |
| datacite.titles.title.fl_str_mv | Minimizing ruin probability - an optimal reinsurance problem using a dynamical setting including dependences |
| dc.contributor.none.fl_str_mv | Moura, Alexandra Oliveira, Carlos Repositório Científico de Acesso Aberto da ULisboa |
| dc.creator.none.fl_str_mv | Botnariuc, Adrialina |
| dc.date.Accepted.fl_str_mv | 2022-10-01T00:00:00Z |
| dc.date.available.fl_str_mv | 2023-02-07T19:06:11Z |
| dc.date.embargoed.fl_str_mv | 2023-02-07T19:06:11Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10400.5/27174 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Instituto Superior de Economia e Gestão |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.fl_str_mv | Ruin probability Excess of lossTreaty Expected value premium principle; Dependent risks |
| dc.title.fl_str_mv | Minimizing ruin probability - an optimal reinsurance problem using a dynamical setting including dependences |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_bdcc |
| description | 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.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. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | masterThesis |
| fulltext.url.fl_str_mv | https://repositorio.ulisboa.pt/bitstreams/72b78291-24df-403a-98a9-897648f0f9f4/download |
| id | ul_d556a1ba8284daf33db77bef0ccd8ded |
| identifier.url.fl_str_mv | http://hdl.handle.net/10400.5/27174 |
| instacron_str | ul |
| institution | Universidade de Lisboa |
| instname_str | Universidade de Lisboa |
| language | eng |
| network_acronym_str | ul |
| network_name_str | Repositório da Universidade de Lisboa |
| oai_identifier_str | oai:repositorio.ulisboa.pt:10400.5/27174 |
| organization_str_mv | urn:organizationAcronym:ul |
| person_str_mv | Botnariuc, Adrialina |
| publishDate | 2022 |
| publisher.none.fl_str_mv | Instituto Superior de Economia e Gestão |
| reponame_str | Repositório da Universidade de Lisboa |
| repository_id_str | urn:repositoryAcronym:ul |
| service_str_mv | urn:repositoryAcronym:ul |
| spelling | engInstituto Superior de Economia e Gestãopt_PTReinsurance 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.application/pdfpt_PTMinimizing ruin probability - an optimal reinsurance problem using a dynamical setting including dependencesBotnariuc, AdrialinaMoura, AlexandraOliveira, CarlosHostingInstitutionOrganizationalRepositório Científico de Acesso Aberto da ULisboae-mailmailto:repositorio@reitoria.ulisboa.ptrepositorio@reitoria.ulisboa.pt2023-02-07T19:06:11Z2022-102022-10-01T00:00:00ZHandlehttp://hdl.handle.net/10400.5/27174http://purl.org/coar/access_right/c_abf2open accessRuin probabilityExcess of lossTreatyExpected value premium principle;Dependent risks424760 bytesliteraturehttp://purl.org/coar/resource_type/c_bdccmaster thesishttp://purl.org/coar/access_right/c_abf2application/pdffulltexthttps://repositorio.ulisboa.pt/bitstreams/72b78291-24df-403a-98a9-897648f0f9f4/download |
| 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 |
| status | SINGLETON |
| subject.fl_str_mv | Ruin probability Excess of lossTreaty Expected value premium principle; Dependent risks |
| title | 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_short | 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 |
| topic | Ruin probability Excess of lossTreaty Expected value premium principle; Dependent risks |
| topic_facet | Ruin probability Excess of lossTreaty Expected value premium principle; Dependent risks |
| url | http://hdl.handle.net/10400.5/27174 |
| visible | 1 |