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.

Longevity risk management through Machine Learning: state of the art

“…This approach aims to overcome the parameter estimation related to SVD, which mainly concerns the lack of nonlinear components, which affects the mortality surface estimation. It is worth noting that the forecasting methods remain the same so that the extrapolation over time is related to canonical models with the classical limitation that are pointed out in Nigri et al (2019), where a DL integration into Lee-Carter model is suggested. They underline the key role of κ t parameter to depict the future nonlinear mortality behavior.…”

Forecasting mortality rates using hybrid Lee–Carter model, artificial neural network and random forest

“…To train the RF model for time series forecasting, we have input the data in the following pattern, where the first three values are corresponding to the input nodes and the forth value defining the desired value for the output node. This training pattern has taken the method applied by Nigri et al [20]. The 3-year data which are the first three values for the input nodes were used, because they are sufficient to reflect the current trend of the mortality rates and can be used to predict the mortality rates for next year which is the forth value defining the desired value for the output node.…”

“…Richman and Wüthrich [19] introduced an extended LC model using the NN algorithms to study the mortality rates in different countries. Nigri et al [20] suggested an alternative approach to the ARIMA process, which is a deep learning integrated LC model based on the Recurrent Neural Network (RNN) with Long Short-Term Memory (LSTM) architecture to predict the future value of parameter.…”

The Daily Container Volumes Prediction of Storage Yard in Port with Long Short-Term Memory Recurrent Neural Network

“…Oehmcke et al [25] also used LSTM and a unique time dimensionality reduction method to reduce computation time and prediction errors. Nigri et al [26] applied LSTM architecture into the Lee-Carter model to improve the predictive accuracy of mortality. e comparison with ARIMA was also given and the superiority of LSTM was demonstrated.…”