Quantile mortality modelling of multiple populations via neural networks

Quantiles of the mortality rates are relevant in life insurance to control longevity risk properly. Recently, Santolino (2020) adapts the framework of the popular Lee-Carter model to compute the conditional quantiles of the mortality rates. The parameters of the quantile Lee-Carter model are fitted on the mortality data of the population of interest, ignoring the information related to the others. In this paper, we show that more robust parameter estimates can be obtained exploiting the mortality experiences of multiple populations. A neural network is employed to calibrate individual quantile Lee-Carter models jointly using all the available mortality data. In this setting, some common network parameters are used to learn the age and period effects of multiple quantile LC models. Numerical experiments performed on all the countries of the Human Mortality Database validate our approach. The predictions obtained considering the median level appear more accurate than those obtained with the mean models; moreover, those at the tail quantile levels capture the future mortality evolution of the populations well.