Actuarial models in demography
Bozikas, Apostolos E.
KeywordsStochastic mortality modelling ; Mortality forecasting ; Lee-Carter model ; CBD model ; Life insurance ; Annuities ; Credibility theory ; Credibility regression ; Random coefficients models ; Multi-population mortality models ; Hierarchical credibility regression ; Crossed classification credibility
During the last decades, a significant increase in life expectancy has been observed in most countries around the world. This change is mainly due to the improvement of living conditions and the development of medical science. Consequently, a serious demographic problem arises from the increasing number of elderly, combined with low fertility rates. Population ageing creates an additional cost for life insurers and annuity providers. In this spirit, the development of efficient methods to model and forecast the mortality rates of a population is a key challenge for actuaries and demographers. This thesis exploits actuarial credibility techniques to propose novel mortality modelling methods, aiming to contribute in more accurate demographic projections. Before introducing these methods, we firstly examine and review the existing modelling techniques. Greek population data are incorporated into the most used stochastic mortality models under a common age-period-cohort framework. The fitting performance of each model is thoroughly evaluated, while projection results for both genders are also illustrated in pricing insurance-related products. In addition, we propose a credibility regression approach with random coefficients to model and forecast the mortality dynamics for populations with limited data. The results on Greek mortality data indicate that credibility regression contributes to more accurate forecasts, compared with those produced from the Lee and Carter (1992) and Cairns et al. (2006) models. Then, the credibility regression model is extended to a multi-level hierarchical credibility regression model for mortality data of multiple populations in a hierarchical form. The forecasting performances between the hierarchical model, the Lee-Carter model and two Lee-Carter extensions for multiple populations are compared for both genders of three northern European countries (Ireland, Norway, Finland). Empirical illustrations show that the proposed method produces more accurate forecasts. Finally, we present a credibility formulation of the Lee-Carter method particularly designed for multi-population mortality modelling. Differently from the standard Lee-Carter methodology, where the time index is assumed to follow an appropriate time series process, herein, the period dynamics of mortality are estimated under a crossed classification credibility framework. The forecasting performances between the proposed model, the Lee-Carter model and two Lee-Carter extensions for multiple populations are compared for both genders of three developed countries (United Kingdom, USA, Japan). The numerical results indicate that the proposed model contributes to more accurate forecasts.