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A common age effect model for the mortality of multiple populations. (English) Zbl 1348.91233

Summary: We introduce a model for the mortality rates of multiple populations. To build the proposed model we investigate to what extent a common age effect can be found among the mortality experiences of several countries and use a common principal component analysis to estimate a common age effect in an age-period model for multiple populations. The fit of the proposed model is then compared to age-period models fitted to each country individually, and to the fit of the model proposed by N. Li and R. Lee [“Coherent mortality forecasts for a group of populations: an extension of the Lee-Carter method”, Demography 42, No. 3, 575–594 (2005; doi:10.1353/dem.2005.0021)].
Although we do not consider stochastic mortality projections in this paper, we argue that the proposed common age effect model can be extended to a stochastic mortality model for multiple populations, which allows to generate mortality scenarios simultaneously for all considered populations. This is particularly relevant when mortality derivatives are used to hedge the longevity risk in an annuity portfolio as this often means that the underlying population for the derivatives is not the same as the population in the annuity portfolio.

MSC:

91D20 Mathematical geography and demography
62P05 Applications of statistics to actuarial sciences and financial mathematics
62H25 Factor analysis and principal components; correspondence analysis
91G20 Derivative securities (option pricing, hedging, etc.)

Software:

AS 211
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References:

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[6] Li, N.; Lee, R., Coherent mortality forecasts for a group of populations: an extension of the Lee-Carter method, Demography, 42, 3, 575-594, (2005)
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