| Name: | Description: | Size: | Format: | |
|---|---|---|---|---|
| 779.37 KB | Adobe PDF |
Authors
Advisor(s)
Abstract(s)
No Brasil, as Entidades Fechadas de Previdência Complementar (EFPC) são denominadas de fundos de
pensões e os planos disponíveis por estas entidades são concedidos a indivíduos com vínculo laboral ou
associativo. A EFPC é quem administra os planos de benefícios, enquanto o atuário é quem realiza a
avaliação atuarial.
Uma avaliação atuarial tem como objetivo estimar o valor que é necessário ter na atualidade para fazer
jus a todos os benefícios previstos no regulamento do plano, tendo como base hipóteses atuariais que
sejam apropriadas à população e às particularidades do plano de benefícios. As hipóteses atuariais
permitirão projetar as obrigações do plano de benefícios no que respeita a população em causa,
realizando-se testes de hipóteses.
O objetivo da realização de testes de hipóteses é compreender a aderência das hipóteses adotadas no ano
anterior à população em causa e, de modo que se consigam resultados estatísticos próximos da realidade,
é necessário que as variáveis utilizadas nos testes sejam testadas com o objetivo de minimizar os riscos
atuariais envolvidos.
Este trabalho de projeto diz respeito à aderência de uma base de dados brasileira às tábuas de mortalidade
utilizadas nas avaliações atuariais do Brasil, sendo que a sua concretização decorreu da realização de
testes de hipóteses, comparando a tábua que está em vigor no Plano de Benefícios ABC com diversas
tábuas de mortalidade.
A componente prática deste trabalho de projeto incidiu na realização de dois testes estatísticos,
especificamente o teste Kolmogorov-Smirnov de comparação de populações e o teste de
Homogeneidade do Qui-Quadrado, para as hipóteses biométricas de Mortalidade Geral e de Mortalidade
de Inválidos.
No Plano de Benefícios ABC, foram testadas as tábuas AT-2000 M&F (tábua em vigor), AT-2000
Básica M&F, BR-EMSsb-V.2015 M&F e BR-EMSsb-V.2021 M&F para o caso da Mortalidade Geral
e para o caso da Mortalidade de Inválidos AT-49 M&F (tábua em vigor), WINKLEVOSS, AT-83 M&F
e RP-2000 Disabled M&F.
Após a aplicação dos testes mencionados, a tábua que se recomendou utilizar na hipótese atuarial de
Mortalidade Geral foi a BR-EMSsb-V.2015 M&F e no caso da Mortalidade de Inválidos foi a tábua em
vigor (AT-49 M&F).
In Brazil, the Closed Entities of Complementary Providence (CECP) are called pension funds, and the plans available from these entities are granted to individuals with employment or association ties. The CECP is the one that manages the benefit plans, while the actuary is the one who performs the actuarial valuation. An actuarial valuation aims to estimate the amount that is required to be entitled to all the benefits provided for in the plan's regulation, based on actuarial assumptions that are appropriate to the population and the particularities of the benefit plan. The actuarial assumptions will make it possible to project the obligations of the benefit plan concerning the population in question, carrying out hypothesis tests. The purpose of hypothesis testing is to understand the adherence of the hypotheses adopted in the previous year to the population and, to obtain statistical results that are close to reality, the variables used in the tests must be tested to minimize the actuarial risks involved. This project concerns the adherence of a Brazilian database to the mortality tables used in actuarial valuations in Brazil, this was accomplished from hypothesis tests, that compared the table in effect in the ABC Benefits Plan with several mortality tables. The practical component of this project focused on performing two statistical tests, specifically the Kolmogorov-Smirnov test for comparing populations and the Chi-square Homogeneity test, for the biometric hypotheses of Mortality and Disabled Mortality. In the ABC Benefits Plan, the AT-2000 M&F (current table), AT-2000 Basic M&F, BR-EMSsb-V.2015 M&F and BR-EMSsb-V.2021 M&F tables were tested for the Mortality and the Disabled Mortality AT49 M&F (current table), WINKLEVOSS, AT-83 M&F, and RP-2000 Disabled M&F. After applying the mentioned tests, the table recommended for the actuarial assumption of Mortality was BR-EMSsb-V.2015 M&F, and for Disabled Mortality was the table in force (AT-49 M&F).
In Brazil, the Closed Entities of Complementary Providence (CECP) are called pension funds, and the plans available from these entities are granted to individuals with employment or association ties. The CECP is the one that manages the benefit plans, while the actuary is the one who performs the actuarial valuation. An actuarial valuation aims to estimate the amount that is required to be entitled to all the benefits provided for in the plan's regulation, based on actuarial assumptions that are appropriate to the population and the particularities of the benefit plan. The actuarial assumptions will make it possible to project the obligations of the benefit plan concerning the population in question, carrying out hypothesis tests. The purpose of hypothesis testing is to understand the adherence of the hypotheses adopted in the previous year to the population and, to obtain statistical results that are close to reality, the variables used in the tests must be tested to minimize the actuarial risks involved. This project concerns the adherence of a Brazilian database to the mortality tables used in actuarial valuations in Brazil, this was accomplished from hypothesis tests, that compared the table in effect in the ABC Benefits Plan with several mortality tables. The practical component of this project focused on performing two statistical tests, specifically the Kolmogorov-Smirnov test for comparing populations and the Chi-square Homogeneity test, for the biometric hypotheses of Mortality and Disabled Mortality. In the ABC Benefits Plan, the AT-2000 M&F (current table), AT-2000 Basic M&F, BR-EMSsb-V.2015 M&F and BR-EMSsb-V.2021 M&F tables were tested for the Mortality and the Disabled Mortality AT49 M&F (current table), WINKLEVOSS, AT-83 M&F, and RP-2000 Disabled M&F. After applying the mentioned tests, the table recommended for the actuarial assumption of Mortality was BR-EMSsb-V.2015 M&F, and for Disabled Mortality was the table in force (AT-49 M&F).
Description
Trabalho de projeto de mestrado, Matemática Aplicada à Economia e Gestão, 2023, Universidade de Lisboa, Faculdade de Ciências
Keywords
Fundo de Pensão Testes de Hipóteses Kolmogorov-Smirnov Qui-Quadrado Tábuas Trabalhos de projeto de mestrado - 2023