Deepening Lee-Carter for longevity projections with uncertainty estimation

Undoubtedly, several countries worldwide endure to experience a continuous increase in life expectancy, extending the challenges of life actuaries and demographers in forecasting mortality. Although several stochastic mortality models have been proposed in past literature, the mortality forecasting research remains a crucial task. Recently, various research works encourage the adequacy of deep learning models to extrapolate suitable pattern within mortality data. Such a learning models allow to achieve accurate point predictions, albeit also uncertainty measures are necessary to support both model estimates reliability and risk evaluations. To the best of our knowledge, machine and deep learning literature in mortality forecasting lack for studies about uncertainty estimation. As new advance in mortality forecasting, we formalizes the deep Neural Networks integration within the Lee-Carter framework, posing a first bridge between the deep learning and the mortality density forecasts. We test our model proposal in a numerical application considering three representative countries worldwide and both genders, scrutinizing two different fitting periods. Exploiting the meaning of both biological reasonableness and plausibility of forecasts, as well as performance metrics, our findings confirm the suitability of deep learning models to improve the predictive capacity of the Lee-Carter model, providing more reliable mortality boundaries also on the long-run.