Time series modelling of Gompertz-Makeham mortality curves: historical analysis, forecasting and life insurance applications

Document description

SA0 dissertation (Fellowship by research). The Continuous Mortality Investigation (CMI) of the Institute and Faculty of Actuaries has for a number of years based its graduated tables of assured life, annuitant and pensioner mortality on Gompertz-Makeham formulae. In this thesis, we consider two-dimensional data sets consisting of the number of deaths and the exposed to risk at a range of ages in a range of calendar years. Having fitted a Gompertz-Makeham model to the data for each calendar year, we fit univariate time series models to represent the behaviour over time of the Gompertz-Makeham parameters. Cohort effects are allowed for by applying a multiplicative factor depending on year of birth to the fitted force of mortality. Prediction intervals for the future parameters of the model are calculated. Sample values of immediate and deferred annuities are presented, based on stochastic mortality simulations and a deterministic interest rate. An application to risk-based capital calculations, under the Individual Capital Assessment (ICA) regime of the Financial Services Authority (FSA), is presented.