Gaussian Process-Based Mortality Monitoring using Multivariate Cumulative Sum Procedures

This paper proposes an online multivariate cumulative sum (MCUSUM) monitoring procedure for detecting changes in mortality dynamics, with direct applications to mortality and longevity risk management for insurers and pension funds. The method is built on Gaussian process (GP) non-parametric mortality forecasts, and performs surveillance in real time by tracking multivariate forecast errors across ages. We develop MCUSUM schemes targeting two practically relevant forms of change: (i) a change in level, corresponding to an abrupt proportional shift in mortality rates, and (ii) a change in trend, corresponding to a shift in the rate of mortality improvement. In both cases, one-sided monitoring rules allow the practitioner to focus on either adverse mortality shocks or adverse longevity developments. By explicitly exploiting dependence between age groups, the proposed multivariate approach improves detection performance relative to collections of univariate control charts. We evaluate the procedure through simulation experiments and empirical applications to recent mortality data from France, Japan, Canada, and the USA, and we further illustrate its use on a real-world life insurance portfolio. Finally, we document the impact of age-pattern changes consistent with rectangularization of mortality curves and discuss how such dynamics can affect prospective monitoring and the interpretation of detection signals.