Abstract
Abstract The Age-Period-Cohort-Improvement (APCI) model is a new addition to the canon of mortality forecasting models. It was introduced by Continuous Mortality Investigation as a means of parameterising a deterministic targeting model for forecasting, but this paper shows how it can be implemented as a fully stochastic model. We demonstrate a number of interesting features about the APCI model, including which parameters to smooth and how much better the model fits to the data compared to some other, related models. However, this better fit also sometimes results in higher value-at-risk (VaR)-style capital requirements for insurers, and we explore why this is by looking at the density of the VaR simulations.
Highlights
Continuous Mortality Investigation (2016b) introduced a new model for fitting to mortality data: the Age-Period-Cohort-Improvement (APCI) model
The purpose of this paper is to present a stochastic implementation of the APCI model for mortality projections, and to compare the performance of this model with various other models sharing similar structural features
It is worth repeating the caution of Currie (2016) that an “oft-overlooked caveat is that it does not follow that an improved fit to data necessarily leads to improved forecasts of mortality”. This was noted in Kleinow and Richards (2016), where the best-fitting ARIMA process for κ in a Lee–Carter model for UK males led to the greatest parameter uncertainty in the forecast, and higher capital requirements under a value-at-risk (VaR) assessment
Summary
Continuous Mortality Investigation (2016b) introduced a new model for fitting to mortality data: the Age-Period-Cohort-Improvement (APCI) model. One option would be to create an arbitrary extension of the projected mortality rates up to (say) age 120 Another alternative is to look at temporary annuities to avoid artefacts arising from the arbitrary extrapolation, as used by Richards et al (2014). We use the latter approach in this paper, and we calculate expectations of time lived and continuously paid temporary annuity factors as follows:. The resulting P-spline-smoothed yield curve reproduces all the main features of Figure 1
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