Neural network Lee–Carter model and the actuarial relevance of longevity risk assessment

Accurate forecasts of mortality and life expectancy values are crucial concerns at various decision-making levels and, in particular, in life insurance. In the context of the Lee–Carter model, we propose an approach to modeling and forecasting mortality based on the use of autoregressive neural network models with exogenous variables combined with a bootstrap scheme, to obtain both point and forecast distributions. Our proposal preserves the LC defining parameters and structure and adds flexibility at reduced costs in terms of complexity and implementability, with respect to other machine learning approaches. It allows to correct and contain the bias that the traditional linear models introduce in mortality predictions, this marking improving results from a statistical perspective and paving the way for promising future developments. The impact of the proposed novel methodology is tested in the actuarial field through case studies in the life annuities framework. In particular, it provides a much more smoothed increase in the uncertainty along the policy duration, which, in terms of risk management, implies less capital set aside against longevity risk while preserving the insurer's resilience.