A quantitative comparison of stochastic mortality models on Italian population data

Mortality models play a basic role in the evaluation of longevity risk by demographers and actuaries. Their performance strongly depends on the different patterns shown by mortality data in different countries. A comprehensive quantitative comparison of the most used methods for forecasting mortality is presented, aimed at evaluating both the goodness of fit and the forecasting performance of these mortality models on Italian demographic data. First, the classical Lee-Carter model is compared to some generalizations that change the order of Singular Value Decomposition approximation and include cohort effects. Then one-way and two-way functional data approaches are considered. Such an analysis extends the current literature on Italian mortality data, on both the number of considered models and their rigorous assessment. Results indicate that generally functional models outperform the classical ones; unfortunately, even if the cohort effect is quite substantial, a suitable procedure for its robust and efficient evaluation is yet to be proposed. To this end, a viable correction for cohort effects is suggested and its performance tested on some of the presented models.