Ricerc@Sapienza

In the field of mortality, the Lee–Carter based approach can be considered the milestone
to forecast mortality rates among stochastic models. We could define a “Lee–Carter model family”
that embraces all developments of this model, including its first formulation (1992) that remains the
benchmark for comparing the performance of future models. In the Lee–Carter model, the kt parameter,
describing the mortality trend over time, plays an important role about the future mortality behavior.
The traditional ARIMA process usually used to model kt shows evident limitations to describe the future
mortality shape. Concerning forecasting phase, academics should approach a more plausible way in
order to think a nonlinear shape of the projected mortality rates. Therefore, we propose an alternative
approach the ARIMA processes based on a deep learning technique. More precisely, in order to catch
the pattern of kt series over time more accurately, we apply a Recurrent Neural Network with a Long
Short-Term Memory architecture and integrate the Lee–Carter model to improve its predictive capacity.
The proposed approach provides significant performance in terms of predictive accuracy and also allow
for avoiding the time-chunks’ a priori selection. Indeed, it is a common practice among academics to
delete the time in which the noise is overflowing or the data quality is insufficient. The strength of
the Long Short-Term Memory network lies in its ability to treat this noise and adequately reproduce it
into the forecasted trend, due to its own architecture enabling to take into account significant long-term
patterns.