A Constrained Nonstationary ACP-GP Model for Mortality Surfaces

We study a constrained nonstationary Gaussian-process framework for mortality surfaces, using German female mortality as the main empirical case study. The proposed methodology combines a low-rank Gaussian-process representation with an age-regime mixture covariance and age-monotonicity constraints enforced through quadratic programming. We consider both a hybrid specification, in which the Gaussian process corrects a structured mean component, and a regime-only specification, in which the Gaussian process acts directly on the full log-mortality surface. This comparison isolates the contribution of the structured mean relative to the covariance design itself. Empirically, the constrained hybrid model produces coherent monotone surfaces and improves on Lee--Carter, while the regime-only specification remains structurally informative but substantially less accurate on the main holdout. Posterior simulation is implemented through exact reflected Hamiltonian Monte Carlo, allowing uncertainty propagation to actuarial quantities such as life expectancy and annuity values. The results support the value of combining shape control, nonstationary covariance modelling, and actuarial interpretability within a unified framework.