Multi-population mortality modelling and forecasting with divergence bounds

Understanding the mortality dynamics and forecasting its future evolution is crucial for insurance companies and governments facing the risk that individuals might live longer than expected (the so-called longevity risk). This paper introduces a neural network model that allows an accurate modelling and forecasting of the mortality rates of many populations. The neural network model we propose is designed to present a fully explainable structure, allowing for understanding how predictions are formulated. Furthermore, the model addresses the problem of measuring and managing the divergence of the long-term forecasts of the mortality rates arising when one decides to model the mortality of two or more populations simultaneously. Indeed, for many models available in the literature, this divergence grows over time, resulting in an ever-increasing trend in the gap in life expectancy among countries that appear unrealistic and biologically unreasonable. The proposed model allows the construction of analytical bounds for this divergence and illustrates that these bounds can be exploited to analyse and measure the dissimilarities between two or more populations and identify opportunities for longevity risk diversification. Numerical experiments performed using all the data from the Human Mortality Database data show that our model produces more accurate mortality forecasts with respect to some well-known stochastic mortality models and allows us to obtain valuable insights about the mortality pattern of the population considered.