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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.

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.) |

### Keywords:

mortality of multiple populations; stochastic mortality model; longevity; basis risk; common age effect### Software:

AS 211
Full Text:
DOI

### References:

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[2] | Flury, B. N., Common principal components in K groups, J. Amer. Statist. Assoc., 79, 388, 892-898, (1984) |

[3] | Flury, B. N.; Constantine, G., Algorithm AS 211: the F-G diagonalization algorithm, J. R. Stat. Soc. Ser. C. Appl. Stat., 34, 2, 177-183, (1985) |

[4] | Kleinow, T.; Cairns, A. J.G., Mortality and smoking prevalence: an empirical investigation in ten developed countries, Br. Actuar. J., 18, 2, 452-466, (2013) |

[5] | Lee, R. D.; Carter, L. R., Modeling and forecasting US mortality, J. Amer. Statist. Assoc., 87, 419, 659-671, (1992) · Zbl 1351.62186 |

[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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