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**An analysis of period and cohort mortality shocks in international data.**
*(English)*
Zbl 1461.91255

Summary: This article uses Bayesian maximum a posteriori (BMAP) estimation to fit a cohort-based mortality model that applies the Gompertz mortality law to fixed cohorts across different periods (rather than the more usual application to fixed periods across different cohorts). Period effects are then estimated as residuals. In this approach, cohort effects can be viewed as a proxy for causes of death with long latency, which have become relatively more important in recent decades in richer countries. We estimate the model independently using male and female adult population mortality data in 31 countries. We are able to associate historical events with many of the observed period and cohort shocks, most notably the 1918 flu epidemic, and find striking geographical and cultural correlations in the results. We find that after 1960, the variance of period mortality shocks has declined by an average factor of 5 in most of the countries we examine. Over the same period, cohort shocks appear to have become a more important factor causing changes in mortality than period shocks. We also find that period and cohort shocks appear to be driven by different underlying factors. Our results have important implications for stochastic mortality modeling, and may explain why stochastic mortality models that rely largely on period mortality shocks struggle to generate sufficient variation in mortality rates. Our results will also be useful to those who construct reinsurance portfolios, those who issue or trade longevity-linked securities, and those who study the origins of human mortality.

### MSC:

91G05 | Actuarial mathematics |

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

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\textit{D. McCarthy} and \textit{P.-L. Wang}, N. Am. Actuar. J. 25, S385--S409 (2021; Zbl 1461.91255)

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