Information Matrix

Actuaries often need to smooth mortality rates. Gompertz (1825) smoothed mortality rates by age and his famous law was a landmark in this area. Figure 1 shows the Gompertz model fitted to CMI assured lives data for ages 20–90 in the year 2002. The Gompertz Law usually breaks down below about age 40 and a more general smooth curve would be appropriate. However, a more general smooth curve would obviously require more parameters than the two for the simple Gompertz model.

With some notable exceptions, such as the Kaplan-Meier estimator, most mortality models contain parameters. In a statistical model these parameters need to be estimated, and it is a natural thing for people to want to place interpretations on those parameter estimates. However, this can be tricky, as parameters in a multi-parameter model are dependent on each other.

Recognising and quantifying mortality differentials is what experience analysis is all about. Whether you calculate traditional A/E ratios, graduate raw rates by formula (Forfar et al. 1988), or fit a statistical model (Richards 2012), the aim is always to find risk factors influencing the level of mortality.

The growing market for longevity risk-transfer means that takers of the risk are keenly interested in the mortality characteristics of the portfolio concerned. The first thing requested by the risk-taker is therefore detailed data on the portfolio's recent mortality experience.  This is ideally data extracted on a policy-by-policy basis.

The motto of the old UK Institute of Actuaries was certum ex incertis, i.e. certainty from uncertainty. I never particularly liked this motto — it implied that certainty can be obtained from uncertainty, whereas uncertainty is all-too-often overlooked.