Information Matrix

Regular readers of this blog (both of them) will have noticed how often we advocate that actuaries use the Kaplan-Meier estimator in their mortality analysis.  While parametric survival models are best for multi-factor models, the Kaplan-Meier estimate is exceptionally useful for visualisation, communication and data-quality checking.

In Richards & Macdonald (2024) we advocate that actuaries use the Kaplan-Meier estimate of the survival curve.  This is not just because it is an excellent visual communication tool, but also because it is a particularly useful data-quality check.

In a (much) earlier blog, Angus introduced the product-integral representation of the survival function:

\[{}_tp_x = \prod_0^t(1-\mu_{x+s}ds),\qquad(1)\]

In Richards et al (2013) we described how actuaries can create mortality tables derived from a portfolio's own experience, rather than relying on tables published elsewhere. There are good reasons why actuaries need to be able to do this, and we came across a stark reminder of this while writing Richards & Macdonald (2024).

Our new book, Modelling Mortality with Actuarial Applications, describes several non-parametric estimators of two quantities:

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.

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.