Bayesian stochastic mortality modelling under serially correlated local effects

Abstract

The vast majority of stochastic mortality models in the academic literature are intended to explain the dynamics underpinning the process by a combination of age, period and cohort e ects. In principle, the more such e ects are included in a stochastic mortality model, the better is the in-sample t to the data. Estimates of those parameters are most usually obtained under some distributional assumption about the occurrence of deaths, which leads to the optimisation of a relevant objective function. The present Thesis develops an alternative framework where the local mortality effect is appreciated, by employing a parsimonious multivariate process for modelling the latent residual e ects of a simple stochastic mortality model as dependent rather than conditionally independent variables. Under the suggested extension the cells of the examined data-set are supplied with a serial dependence structure by relating the residual terms through a simple vector autoregressive model. The method is applicable for any of the popular mortality modelling structures in academia and industry, and is accommodated herein for the Lee-Carter and Cairns-Blake-Dowd models. The additional residuals model is used to compensate for factors of a mortality model that might mostly be a ected by local e ects within given populations. By using those two modelling bases, the importance of the number of factors for a stochastic mortality model is emphasised through the properties of the prescribed residuals model. The resultant hierarchical models are set under the Bayesian paradigm, and samples from the joint posterior distribution of the latent states and parameters are obtained by developing Markov chain Monte Carlo algorithms. Along with the imposed short-term dynamics, we also examine the impact of the joint estimation in the long-term factors of the original models. The Bayesian solution aids in recognising the di erent levels of uncertainty for the two naturally distinct type of dynamics across di erent populations. The forecasted rates, mortality improvements, and other relevant mortality dependent metrics under the developed models are compared to those produced by their benchmarks and other standard stochastic mortality models in the literature.