Backtesting stochastic mortality models by prediction interval-based metrics

Human lifespan increments represent one of the main current risks for governments and pension and health benefits providers. Longevity societies imply financial sustainability challenges to guarantee adequate socioeconomic conditions for all individuals for a longer period. Consequently, modelling population dynamics and projecting future longevity scenarios are vital tasks for policymakers. As an answer, the demographic and the actuarial literature have been introduced and compared to several stochastic mortality models, although few studies have thoroughly tested the uncertainty concerning mortality projections. Forecasting mortality uncertainty levels have a central role since they reveal the potential, unexpected longevity rise and the related economic impact. Therefore, the present study poses a methodological framework to backtest uncertainty in mortality projections by exploiting uncertainty metrics not yet adopted in mortality literature. Using the data from the Human Mortality Database of the male and female populations of five countries, we present some numerical applications to illustrate how the proposed criterion works. The results show that there is no mortality model overperforming the others in all cases, and the best model choice depends on the data considered.