Information Matrix

In a recent paper presented to the Faculty of Actuaries, Stephen Richards and I discussed model risk and showed how it can have a material impact on mortality forecasts.  Different models have different features, some more desirable than others.  This post illustrates a particular problem with the original Lee-Carter model, and shows how it can be combatted via smoothing.  The choice of which parameters to smooth in the Lee-Carter model leads to a general family

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

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:

\[r = \frac{D-E}{\sqrt{E}}\qquad(1)\]