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**On age-period-cohort parametric mortality rate projections.**
*(English)*
Zbl 1231.91195

Summary: An enhanced version of the Lee-Carter modelling approach to mortality forecasting, which has been extended to include an age modulated cohort index in addition to the standard age modulated period index, is described and tested for prediction robustness. Life expectancy and annuity value predictions, at pensioner ages and for various periods are compared, both with and without the age modulated cohort index, for the England & Wales male mortality experience. The simulation of prediction intervals for these indices of interest is discussed in detail.

### MSC:

91B30 | Risk theory, insurance (MSC2010) |

91B82 | Statistical methods; economic indices and measures |

### Keywords:

mortality forecasting; age-period-cohort effects; forecast statistics; back-fitting; data truncation
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\textit{S. Haberman} and \textit{A. Renshaw}, Insur. Math. Econ. 45, No. 2, 255--270 (2009; Zbl 1231.91195)

### References:

[1] | Cairns, A. J.G.; Blake, D.; Dowd, K., A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration, Journal of Risk and Insurance, 73, 687-718 (2006) |

[2] | Cairns, A. J.G.; Blake, D.; Dowd, K.; Coughlan, G. D.; Epstein, D.; Ong, A.; Balevich, I., A quantitative comparison of stochastic mortality models using data from England & Wales and the United States, North American Actuarial Journal, 13, 1, 1-35 (2009) · Zbl 1484.91376 |

[4] | Coale, A.; Kisker, E. E., Defects in data on old age mortality in the United States: New procedures for calculating approximately accurate mortality schedules and life tables at the highest ages, Asian and Pacific Population Forum, 4, 1-31 (1990) |

[5] | Delwarde, A.; Denuit, M.; Eilers, P., Smoothing the Lee-Carter and Poisson log-bilinear models for mortality forecasting: A penalised log-likelihood approach, Statistical Modelling, 7, 385-401 (2007) |

[6] | Denuit, M., Distribution of random future life expectancies in log-bilinear mortality projection models, Lifetime Data Analysis, 13, 381-397 (2007) · Zbl 1331.62399 |

[7] | Denuit, M.; Goderniaux, A.-C., Closing and projecting life tables using log-linear models, Bulletin of the Swiss Association of Actuaries, 1, 29-48 (2005) · Zbl 1333.62251 |

[9] | Hamilton, J. D., Times Series Analysis, Princeton University Press (1994) |

[10] | Janssen, F.; Kunst, A., The choice among past trends as a basis for prediction of future trends in old-age mortality, Population Studies, 61, 315-326 (2007) |

[11] | Lee, R., The Lee-Carter method for forecasting mortality, with various extensions and applications, North American Actuarial Journal, 4, 1, 80-93 (2000) · Zbl 1083.62535 |

[12] | Lee, R.; Carter, L., Modelling and forecasting the time series of US mortality, Journal of the American Statistical Association (with discussion), 87, 659-671 (1992) |

[13] | Renshaw, A. E.; Haberman, S., Lee-Carter mortality forecasting with age-specific enhancement, Insurance: Mathematics and Economics, 33, 255-272 (2003) · Zbl 1103.91371 |

[14] | Renshaw, A. E.; Haberman, S., A cohort-based extension to the Lee-Carter model for mortality reduction factors, Insurance: Mathematics and Economics, 38, 556-570 (2006) · Zbl 1168.91418 |

[15] | Renshaw, A. E.; Haberman, S., On simulation-based approaches to risk measurement in mortality with specific reference to Poisson Lee-Carter modelling, Insurance: Mathematics and Economics, 42, 797-816 (2008) · Zbl 1152.91598 |

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