Information Matrix

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:

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

In the distant past, individual insurers had relatively modest business volumes and the industry needed to pool its data to get an overall data set of sufficient credibility. In the U.K., the mechanism for pooling mortality data is the CMI. An earlier blog mentioned some challenges surrounding the changing volumes of data in the CMI assured lives data set.

Members of defined-benefit pension schemes can often retire early if they are in poor health.  Unsurprisingly, such ill-health retirements exhibit higher mortality rates than those who retire at the normal scheme age.

In February 2009 a variation on the Lee-Carter model for smoothing and projecting mortality rates was presented to the Faculty of Actuaries.  A key question for any projection model is whether the process being modelled is stable.  If the process is not stable, then a model assuming it is stable will give misleading projections.  Equally, a model which makes projections by placing a greater emphasis on recent data will be better able to identify a change in tempo of the underlying p