Frailty-based Lee–Carter family of stochastic mortality models

In the actuarial literature, frailty is defined to be the unobserved variable which encompasses all the factors affecting human mortality other than gender and age. Heterogeneity in individual frailty can play a significant role in population mortality dynamics. In the present paper, we identify the main latent factors that explain the frailty component, in order to clarify its role in mortality projections. We show, using longitudinal survey data, that frailty is mainly due to co-morbidities that impact on the process of deterioration in terms of the human body’s physiological capacity. Accordingly, we provide frailty-based stochastic models for projecting mortality based on the Lee–Carter family of models. We propose several versions that consider frailty both as an age-dependent and a time-dependent factor and also combining the interaction effects of age and time in comparison with the general level of mortality, and compare the resulting mortality projections using data from England.