Distribution of the random future life expectancies in log-bilinear mortality projection models |
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Authors: | Michel Denuit |
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Institution: | (1) Institut de Statistique & Institut des Sciences Actuarielles, Université Catholique de Louvain, Louvain-la-Neuve, Belgium |
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Abstract: | Projected life tables are obtained from forecasting methods and account for future improvements in longevity. Since the future
path of mortality is unknown, working with projected life tables makes the survival probabilities stochastic. The resulting
demographic indicators in turn become random variables. This paper aims to study the distribution of period and cohort life
expectancies derived from projected life tables. To fix the ideas, we adopt here the standard Lee–Carter framework, where
the future forces of mortality are decomposed in a log-bilinear way. Exact formulas are derived for period life expectancies,
and approximations are proposed for cohort life expectancies. In the latter case, numerical illustrations based on Belgian
population data show that the relative accuracy is remarkable. |
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Keywords: | Lee– Carter model Period Cohort Life expectancy Comonotonicity |
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