Constrained Kriging for Smoothing and Forecasting Mortality Rates

Mortality surface is a function of age and year with the main characteristic of being increasing in age direction from a given age. One of the major challenges of its construction is to take this last specificity into account. In this paper, we propose to use constrained Kriging for such construction. Our approach is based on the finite-dimensional approximation of the Gaussian process. We first show the ability of the constrained Kriging to construct mortality surfaces and then compare its performance against classical Kriging models with trend functions such as those used in [LRZ18]. Our empirical study based on mortality data from three countries (France, Italy, and Germany) showed the need to add a constraint of convexity in age direction and illustrated through an RMSE criterion that the constrained Kriging provided better results in terms of out-of-sample forecasting.