Upper and lower bounds for annuities and life insurance from incomplete mortality data
ABSTRACT This study aimed to set upper and lower bounds for the expected present value of whole life annuities and whole life insurance policies from incomplete mortality data, generalizing previous results on life expectancy. Since its inception, in the 17th century, actuarial science has been devoted to the study of annuities and insurance plans. Thus, setting intervals that provide an initial idea about the cost of these products using incomplete mortality data represents a theoretical contribution to the area and this may have major applications in markets lacking historical records or those having little reliability of mortality data, as well as in new markets still poorly explored. For both the continuous and discrete cases, upper and lower bounds were constructed for the expected present value of whole life annuities and whole life insurance policies, contracted by a person currently aged x, based on information about the expected present value of these respective financial products subscribed to by a person of age x + n and the probability that an individual of age x survives to at least age x + n. Through the bounds of a continuous annuity, in an environment where the instantaneous interest rate is equal to zero, the results shown also set bounds for the complete life expectancy, which implies that the contribution of this research generalizes previous results in the literature. It was also found that, for both annuities and insurance plans, the length of constructed intervals increases as the data gap size increases and it decreases as the survival curve becomes more rectangular. Illustratively, bounds for life expectancy at 40 and 60 years of age, for the 10 municipalities showing the highest life expectancy at birth in Brazil in 2010, were constructed by using data available in the Atlas of Human Development in Brazil.
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Universidade de São Paulo, Faculdade de Economia, Administração e Contabilidade, Departamento de Contabilidade e Atuária
2019
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oai:scielo:S1519-707720190002002822019-04-03Upper and lower bounds for annuities and life insurance from incomplete mortality dataSouza,Filipe Costa de actuarial mathematics actuarial science annuities life insurance mortality table ABSTRACT This study aimed to set upper and lower bounds for the expected present value of whole life annuities and whole life insurance policies from incomplete mortality data, generalizing previous results on life expectancy. Since its inception, in the 17th century, actuarial science has been devoted to the study of annuities and insurance plans. Thus, setting intervals that provide an initial idea about the cost of these products using incomplete mortality data represents a theoretical contribution to the area and this may have major applications in markets lacking historical records or those having little reliability of mortality data, as well as in new markets still poorly explored. For both the continuous and discrete cases, upper and lower bounds were constructed for the expected present value of whole life annuities and whole life insurance policies, contracted by a person currently aged x, based on information about the expected present value of these respective financial products subscribed to by a person of age x + n and the probability that an individual of age x survives to at least age x + n. Through the bounds of a continuous annuity, in an environment where the instantaneous interest rate is equal to zero, the results shown also set bounds for the complete life expectancy, which implies that the contribution of this research generalizes previous results in the literature. It was also found that, for both annuities and insurance plans, the length of constructed intervals increases as the data gap size increases and it decreases as the survival curve becomes more rectangular. Illustratively, bounds for life expectancy at 40 and 60 years of age, for the 10 municipalities showing the highest life expectancy at birth in Brazil in 2010, were constructed by using data available in the Atlas of Human Development in Brazil.info:eu-repo/semantics/openAccessUniversidade de São Paulo, Faculdade de Economia, Administração e Contabilidade, Departamento de Contabilidade e AtuáriaRevista Contabilidade & Finanças v.30 n.80 20192019-08-01info:eu-repo/semantics/articletext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1519-70772019000200282en10.1590/1808-057x201807320 |
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Souza,Filipe Costa de Upper and lower bounds for annuities and life insurance from incomplete mortality data |
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Upper and lower bounds for annuities and life insurance from incomplete mortality data |
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Upper and lower bounds for annuities and life insurance from incomplete mortality data |
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Upper and lower bounds for annuities and life insurance from incomplete mortality data |
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Upper and lower bounds for annuities and life insurance from incomplete mortality data |
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Upper and lower bounds for annuities and life insurance from incomplete mortality data |
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upper and lower bounds for annuities and life insurance from incomplete mortality data |
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ABSTRACT This study aimed to set upper and lower bounds for the expected present value of whole life annuities and whole life insurance policies from incomplete mortality data, generalizing previous results on life expectancy. Since its inception, in the 17th century, actuarial science has been devoted to the study of annuities and insurance plans. Thus, setting intervals that provide an initial idea about the cost of these products using incomplete mortality data represents a theoretical contribution to the area and this may have major applications in markets lacking historical records or those having little reliability of mortality data, as well as in new markets still poorly explored. For both the continuous and discrete cases, upper and lower bounds were constructed for the expected present value of whole life annuities and whole life insurance policies, contracted by a person currently aged x, based on information about the expected present value of these respective financial products subscribed to by a person of age x + n and the probability that an individual of age x survives to at least age x + n. Through the bounds of a continuous annuity, in an environment where the instantaneous interest rate is equal to zero, the results shown also set bounds for the complete life expectancy, which implies that the contribution of this research generalizes previous results in the literature. It was also found that, for both annuities and insurance plans, the length of constructed intervals increases as the data gap size increases and it decreases as the survival curve becomes more rectangular. Illustratively, bounds for life expectancy at 40 and 60 years of age, for the 10 municipalities showing the highest life expectancy at birth in Brazil in 2010, were constructed by using data available in the Atlas of Human Development in Brazil. |
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Universidade de São Paulo, Faculdade de Economia, Administração e Contabilidade, Departamento de Contabilidade e Atuária |
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2019 |
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http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1519-70772019000200282 |
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