A Deep Learning Integrated Lee–Carter Model

Abstract

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 κ t parameter, describing the mortality trend over time, plays an important role about the future mortality behavior. The traditional ARIMA process usually used to model κ t 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 κ t 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.