The Neural Network Lee–Carter Model with Parameter Uncertainty: The Case of Italy

One of the main challenges for life actuaries is modeling and predicting the future mortality evolution. To this end, several stochastic mortality models have been proposed in literature, starting from the pivotal approach of the Lee–Carter model. These models essentially use the ARIMA processes to forecast the future mortality trends. Recently, some research works have shown the adequacy of the deep learning techniques to improve mortality modeling, obtaining competitive and outperforming forecasts compared to the ARIMA. The present work focuses on the application of a recurrent neural network, the Long Short-Term Memory (LSTM), in the Lee–Carter model framework. The LSTM has an architecture specifically designed to model and predict sequential data, such as time series, well capturing hidden patterns within data related to events that may be far from each other. In mortality modeling, this means that the forecasted mortality rates take into account the hidden features of the past phenomenon not always adequately captured by the ARIMA. We extend the approach proposed in Nigriet al. (Risks 7(1), 33 (2019)), performing a point forecasting of the Lee–Carter time-index through LSTM and deriving the related prediction interval representing the LSTM’s parameter uncertainty.