##
**A Bayesian approach to modeling and projecting cohort effects.**
*(English)*
Zbl 1461.91245

Summary: One of the key motivations in the construction of ever more sophisticated mortality models was the realization of the importance of “cohort effects” in the historical data. However, these are often difficult to estimate robustly, due to the identifiability issues present in age/period/cohort mortality models, and exhibit spurious features for the most recent years of birth, for which we have little data. These can cause problems when we project the model into the future. In this study, we show how to ensure that projected mortality rates from the model are independent of the arbitrary identifiability constraints needed to identify the cohort parameters. We then go on to develop a Bayesian approach for projecting the cohort parameters that allows fully for uncertainty in the recent parameters due to the lack of information for these years of birth, which leads to more reasonable projections of mortality rates in future.

### MSC:

91G05 | Actuarial mathematics |

62P05 | Applications of statistics to actuarial sciences and financial mathematics |

PDF
BibTeX
XML
Cite

\textit{A. Hunt} and \textit{D. Blake}, N. Am. Actuar. J. 25, S235--S254 (2021; Zbl 1461.91245)

### References:

[1] | Blake, D.; Burrows, W., Survivor bonds: Helping to hedge mortality risk, The Journal of Risk and Insurance, 68, 2, 339-48 (2001) |

[2] | Blake, D.; Cairns, A. J.; Dowd, K., Living with mortality: Longevity bonds and other mortality-linked securities, British Actuarial Journal, 12, 1, 153-97 (2006) |

[3] | Cairns, A. J.; Blake, D.; Dowd, K., Pricing death: Frameworks for the valuation and securitization of mortality risk, ASTIN Bulletin, 36, 1, 79-120 (2006) · Zbl 1162.91403 |

[4] | Cairns, A. J.; Blake, D.; Dowd, K.; Coughlan, G. D.; Epstein, D.; Khalaf-Allah, M., Mortality density forecasts: An analysis of six stochastic mortality models, Insurance: Mathematics and Economics, 48, 3, 355-67 (2011) |

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

[6] | Cairns, A. J.; Blake, D.; Dowd, K.; Kessler, A., Phantoms never die: Living with unreliable population data, Journal of the Royal Statistical Society: Series A (Statistics in Society) (2015) |

[7] | Dawson, P.; Dowd, K.; Cairns, A. J.; Blake, D., Survivor derivatives: A consistent pricing framework, Journal of Risk and Insurance, 77, 3, 579-96 (2010) |

[8] | Dowd, K., Survivor bonds: A comment on Blake and Burrows, Journal of Risk & Insurance, 70, 2, 339-48 (2003) |

[9] | Dowd, K.; Cairns, A. J.; Blake, D., Mortality-dependent financial risk measures, Insurance: Mathematics and Economics, 38, 3, 427-40 (2006) · Zbl 1168.91411 |

[10] | Dowd, K.; Cairns, A. J. G.; Blake, D.; Coughlan, G. D.; Khalaf-Allah, M., A gravity model of mortality rates for two related populations, North American Actuarial Journal, 15, 2, 334-56 (2011) · Zbl 1228.91032 |

[11] | Fetiveau, C.; Jia, C., Longevity risk hedging with population based index solution - A study of basis risk based on England & Wales population (2014), Tech. rep., Deutsche Bank |

[12] | Haberman, S.; Renshaw, A., A comparative study of parametric mortality projection models, Insurance: Mathematics and Economics, 48, 1, 35-55 (2011) |

[13] | Mortality Database (Shkolnikov, V., and M. Barbieri, with J. Wilmoth) (2014) |

[14] | Hunt, A.; Blake, D., A general procedure for constructing mortality models, North American Actuarial Journal, 18, 1, 116-38 (2014) · Zbl 1412.91045 |

[15] | Hunt, A.; Blake, D., Modelling longevity bonds: Analysing the Swiss Re Kortis Bond, Insurance: Mathematics and Economics, 63, 12-29 (2015) · Zbl 1348.91150 |

[16] | (2020) |

[17] | (2020) |

[18] | (2020) |

[19] | (2020) |

[20] | (2020) |

[21] | Kaas, R.; Goovaerts, M.; Dhaene, J.; Denuit, M. M., Modern actuarial risk theory (2008) · Zbl 1148.91027 |

[22] | Koissi, M.; Shapiro, A.; Hognas, G., Evaluating and extending the Lee-Carter model for mortality forecasting: Bootstrap confidence interval, Insurance: Mathematics and Economics, 38, 1, 1-20 (2006) · Zbl 1098.62138 |

[23] | Mavros, G.; Cairns, A. J.; Kleinow, T.; Streftaris, G., A parsimonious approach to stochastic mortality modelling with dependent residuals (2014), Heriot-Watt University: Heriot-Watt University, Edinburgh |

[24] | Murphy, M., The “golden generations” in historical context, British Actuarial Journal, 15, S1, 151-84 (2009) |

[25] | Murphy, M., Re-examining the dominance of birth cohort effects on mortality, Population and Development Review, 36, 2, 365-90 (2010) |

[26] | Pedroza, C., A Bayesian forecasting model: Predicting U.S. male mortality, Biostatistics, 7, 4, 530-50 (2006) · Zbl 1170.62397 |

[27] | Plat, R., On stochastic mortality modeling, Insurance: Mathematics and Economics, 45, 3, 393-404 (2009) · Zbl 1231.91227 |

[28] | Reichmuth, W.; Sarferaz, S., Bayesian demographic modeling and forecasting: An application to U.S. mortality (2008), Humbolt University: Humbolt University, Berlin |

[29] | Richards, S. J., Detecting year-of-birth mortality patterns with limited data, Journal of the Royal Statistical Society: Series A (Statistics in Society), 171, 1, 279-98 (2008) |

[30] | Willets, R., Mortality in the next millennium (1999), Staple Inn Actuarial Society |

[31] | Willets, R., The cohort effect: Insights and explanations, British Actuarial Journal, 10, 4, 833-77 (2004) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.