
Stephen Richards
Articles written by Stephen Richards
A Scottish question
Out for the count
Stabilising projections
With many stochastic models of mortality, projections of future mortality rates are done using a time series. In a landmark paper, Currie, Durban and Eilers (2004) introduced the idea of using P-splines as an alternative means of generating a forecast. P-splines formed the basis of a projection tool the CMI made fr
Partial buy-outs
Expectations v. extrapolations
Discrimination
Self-selection
Actuaries valuing pension liabilities need to make projections of future mortality rates. The future is inherently uncertain, so it is best to use stochastic models of mortality. Unfortunately, such models require a long enough time series, but few (if any) portfolios have such data. In the UK actuaries typically rely on one of two alternative data sets: the England & Wales data from the ONS, which goes back to 1961, or the "assured lives" data from the CMI, wh
Measuring obesity
Are annuities expensive enough?
Residual concerns
One of the most important means of checking a model's fit is to look at the residuals, i.e. the standardised differences between the actual data observed and what the model predicts. One common definition, known as the Pearson residual, is as follows:
\[r = \frac{D-E}{\sqrt{E}}\qquad(1)\]