Robust mortality forecasting in the presence of outliers

Stochastic mortality models are important for a variety of actuarial tasks, from best-estimate forecasting to assessment of risk capital requirements. However, the mortality shock associated with the Covid-19 pandemic of 2020 distorts forecasts by (i) biasing parameter estimates, (ii) biasing starting points, and (iii) inflating variance. Stochastic mortality models therefore require outlier-robust methods for forecasting. Objective methods are required, as outliers are not always obvious on visual inspection. In this paper we look at the robustification of three broad classes of forecast: univariate time indices (such as in the Lee-Carter and APC models); multivariate time indices (such as in the Cairns-Blake-Dowd and newer Tang-Li-Tickle model families); and penalty projections (such as with the 2D P-spline model). In each case we identify outliers using quantitative methods, then co-estimate outlier effects along with other parameters. Doing so removes the bias and distortion to the forecast caused by a mortality shock, while providing a robust starting point for projections. Illustrations are given for various models in common use.