Age-Dependent Multi-Cohort Affine Mortality Models with Cohort Correlation
- Publisher:
- ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD
- Publication Type:
- Journal Article
- Citation:
- North American Actuarial Journal, 2026, ahead-of-print, (ahead-of-print)
- Issue Date:
- 2026-01-01
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Continuous-time affine mortality models are useful in the analysis of age-cohort mortality rates as they yield a closed-form expression for survival curves, which are consistent with the dynamics of latent factors driving mortality and are well-suited for finance and insurance applications. We extend and improve these mortality models by introducing age dependence of mortality rates and correlation between cohorts. We propose and compare two classes of age-dependent mortality models, namely the age-dependent coefficient model and the age-dependent factor model. Specifically, we assess both Gaussian and Cox–Ingersoll–Ross (CIR)–type models for each category of age-dependent models. Both categories of age-dependent models involve age and calendar time, which in turn specify the cohort. Thus, our models admit an analytical form for the instantaneous correlation between mortality rates of different cohorts. Moreover, we propose two improvements to the parameter estimation process. First, to improve the estimation of cohort correlations, we regularize the parameter estimation by adding a penalty term which penalizes larger differences between empirical and estimated correlations. Second, we develop and assess a method to include incomplete cohorts into the Kalman filtering algorithm for parameter estimation. By incorporating age dependence and using incomplete cohort mortality data, we improve the goodness of fit and produce more reasonable out-of-sample forecasts of survival probabilities. We also show that regularization produces more realistic correlations between cohorts for varying age differences. Our results show that, under most circumstances, the correlation between cohorts decreases as the age difference increases.
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