Deep Learning na gestão de risco de longevidade: o Modelo N-HITS nas projeções de mortalidade e avaliação dos q-forwards

Abstract

Longevity risk, associated with the possibility that the population may live longer than

initially expected, poses an increasing challenge to the solvency of insurance compa- nies, pension funds, and social security systems. In this context, mortality-linked deriv- atives such as q-forwards emerge as instruments designed to transfer and manage

this risk, whose effectiveness depends on the accuracy of mortality projections. Tradi- tionally, these calculations are performed using statistical models such as the Lee–

Carter model, which, although commonly used, show limitations in capturing nonlinear patterns. This study aims to analyze the relative performance of the Neural Hierarchical Interpolation for Time Series Forecasting (N-HiTS) model, compared to the statistical Lee–Carter (LC) and the Multilayer Perceptron (MLP), in forecasting mortality rates for

France and Australia and in pricing q-forwards. Mortality data from France and Aus- tralia were obtained from the Human Mortality Database (1950–2018), divided into

training (1950–2008) and testing (2009–2018) periods. Model performance was eval- uated using MAPE and RMSE metrics and through their application to q-forward pric- ing. The results indicate that N-HiTS consistently outperformed the comparative mod- els, reducing MAPE by up to 31% and RMSE by up to 43% in France, while maintaining

stable predictive accuracy in Australia, even under more volatile conditions. In the pric- ing of q-forwards, the model generated more consistent values, approximately 5–7%

higher at critical ages (70–80 years), correcting the Lee–Carter model’s tendency to

underprice longevity risk. It is concluded that N-HiTS enhances the accuracy of mor- tality projections and improves the effectiveness of mortality-linked derivatives, offering

a methodological contribution to longevity risk management and supporting the finan- cial sustainability of actuarial and pension institutions.