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Optimal reinsurance maximising the expected utility of the insurer’s surplus in a Cox process

2022-10Master thesis Open access
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dc.contributor.advisorMoura, Alexandra
dc.contributor.advisorGuerra, Manuel
dc.contributor.authorFerreira, João Oliveira
dc.date.accessioned2023-01-10T10:43:10Z
dc.date.available2023-01-10T10:43:10Z
dc.date.issued2022-10
dc.descriptionMestrado Bolonha em Mathematical Financept_PT
dc.description.abstractThe main objective of this thesis1 is to study the optimal reinsurance problem, from the ceding insurance company’s perspective. The direct insurer has monotonic preferences (more wealth is better), limited resources and rates his wealth by a non-decreasing concave utility function. The wealth of the cedent is modelled considering a modified version of the classical Cramer-Lundberg surplus process. A Cox process with a Poisson shot noise intensity is used ´ to model the claim arrivals, introducing dependencies between inter-arrival times. Proportional reinsurance treaties are considered and the percentage that the first-line insurance company wants to cede for each claim is denoted as α. Therefore, the cedent seeks the optimal percentage αˆ that maximises his expected utility of wealth in any given year. Furthermore, an implicit solution, the optimal condition is obtained. The results show that the optimal level of reinsurance depends on the relationship between the first-line insurer’s expected utility of wealth and the level of reinsurance.pt_PT
dc.description.abstractO foco principal desta tese2 e estudar o problema do resseguro ´ otimo sob a ´ otica da se- ´ guradora cedente. Esta seguradora tem preferencias monot ˆ onicas (mais riqueza ´ e melhor), re- ´ cursos limitados e a sua riqueza segue uma func¸ao de utilidade c ˜ oncava n ˆ ao decrescente. O ˜ excedente do segurador e modelado considerando uma vers ´ ao modificada do processo cl ˜ assico ´ de excedente de Cramer-Lundberg ´ . O processo Cox com Poisson de intensidade shot noise, e´ utilizado para modelar a intensidade de chegadas de sinistros, introduzindo dependencias entre ˆ os mesmos. Sao considerados contratos de resseguro proporcional e a percentagem que a segu- ˜ radora de primeira linha quer ceder para cada sinistro e denotado como ´ α. Portanto, a cedente procura uma percentagem otima, ´ αˆ, que maximize a utilidade esperada da sua riqueza, para um determinado ano. Por ultimo, ´ e obtido uma soluc¸ ´ ao impl ˜ ´ıcita, da qual seguem as condic¸oes de otimalidade. Os ˜ resultados mostram que o n´ıvel otimo de resseguro depende da relac¸ ´ ao entre a utilidade esper- ˜ ada da riqueza da seguradora de primeira linha e o n´ıvel de resseguro.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationFerreira, João Oliveira (2022). “Optimal reinsurance maximising the expected utility of the insurer’s surplus in a Cox process”. Dissertação de Mestrado. Universidade de Lisboa. Instituto Superior de Economia e Gestãopt_PT
dc.identifier.urihttp://hdl.handle.net/10400.5/26789
dc.language.isoengpt_PT
dc.publisherInstituto Superior de Economia e Gestãopt_PT
dc.relationOptimal Reinsurance with dependencies
dc.subjectCox Processpt_PT
dc.subjectReinsurancept_PT
dc.subjectExpected Utilitypt_PT
dc.subjectInsurer’s Surpluspt_PT
dc.subjectQuota Sharept_PT
dc.subjectProcesso Coxpt_PT
dc.subjectResseguropt_PT
dc.subjectUtilidade Esperadapt_PT
dc.subjectExcedente do Seguradorpt_PT
dc.subjectResseguro de Quotaspt_PT
dc.titleOptimal reinsurance maximising the expected utility of the insurer’s surplus in a Cox processpt_PT
dc.typemaster thesis
dspace.entity.typePublication
oaire.awardTitleOptimal Reinsurance with dependencies
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/3599-PPCDT/EXPL%2FEGE-ECO%2F0886%2F2021/PT
oaire.fundingStream3599-PPCDT
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsopenAccesspt_PT
rcaap.typemasterThesispt_PT
relation.isProjectOfPublication150ed015-9d19-4531-b218-0ae96e599810
relation.isProjectOfPublication.latestForDiscovery150ed015-9d19-4531-b218-0ae96e599810

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