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Posts feedThe product integral in practice
In a (much) earlier blog, Angus introduced the product-integral representation of the survival function:
\[{}_tp_x = \prod_0^t(1-\mu_{x+s}ds),\qquad(1)\]
Doing our homework
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).
The Karma of Kaplan-Meier
Our new book, Modelling Mortality with Actuarial Applications, describes several non-parametric estimators of two quantities:
Spotting hidden data-quality issues
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.
Early retirements
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.
Are you allergic to statistical models?
Or do you know someone who is? Some people are uncomfortable with the idea of statistical models, especially ones with parameters.