Bayesian mortality forecasting with overdispersion. (English) Zbl 1406.62130

Summary: The ability to produce accurate mortality forecasts, accompanied by a set of representative uncertainty bands, is crucial in the planning of public retirement funds and various life-related businesses. In this paper, we focus on one of the drawbacks of the Poisson Lee-Carter model [N. Brouhns et al., Insur. Math. Econ. 31, No. 3, 373–393 (2002; Zbl 1074.62524)] that imposes mean-variance equality, restricting mortality variations across individuals. Specifically, we present two models to potentially account for overdispersion. We propose to fit these models within the Bayesian framework for various advantages, but primarily for coherency. Markov Chain Monte Carlo (MCMC) methods are implemented to carry out parameter estimation. Several comparisons are made with the Bayesian Poisson Lee-Carter model [C. Czado et al., ibid. 36, No. 3, 260–284 (2005; Zbl 1110.62142)] to highlight the importance of accounting for overdispersion. We demonstrate that the methodology we developed prevents over-fitting and yields better calibrated prediction intervals for the purpose of mortality projections. Bridge sampling is used to approximate the marginal likelihood of each candidate model to compare the models quantitatively.


62P05 Applications of statistics to actuarial sciences and financial mathematics
62M20 Inference from stochastic processes and prediction
62N05 Reliability and life testing
91D20 Mathematical geography and demography
91B30 Risk theory, insurance (MSC2010)
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