Faculty of Actuarial Science & Insurance Seminar with Andres Villegas (University of New South Wales, Australia).

Abstract
Humanity has made, and continues to make, significant progress in averting and delaying death, which burdens society with increased longevity costs. This has brought to the fore the critical importance of mortality forecasting for actuaries and demographers. Consequently, numerous mortality models have been proposed, with the most popular and commonly-referenced models belonging to a generalised age-period-cohort framework. These models decompose observed historical mortality rates across the dimensions of age, period, and cohort (or year-of-birth), which can then be extrapolated to forecast future outcomes. Recently, a large number of models have been proposed within this framework, many of which are over-parameterised and produce spurious forecasts, particularly over long horizons and for noisy data sets.

In this paper we exploit data analytics techniques to provide a comprehensive framework to construct, select, and evaluate discrete-time age-period-cohort mortality models. To devise this robust framework, we leverage two key statistical learning tools – cross validation and regularisation – to draw as much insight as possible from limited data sets. We first propose a cross validation framework for model selection, which can be tailored to determine the features of mortality models that are desired for different actuarial applications, including period and cohort-based forecasting. This enables the answering of questions regarding the effects of population size and structure, age, and forecasting basis and horizon on the preferred model selection. We also present a regularisation approach to construct bespoke mortality models by automatically selecting the most appropriate parametric forms to best describe and forecast particular data sets, using a trade-off between complexity and parsimony. We illustrate this using empirical data from the Human Mortality Database and simulated data sets.