If this and other recent blogs have a historical flavour, the reason is the 200th anniversary of the 1825 paper by Benjamin Gompertz that introduced his eponymous law of mortality. In the course of his own researches, Stephen drew to my attention a short letter published by Wilhelm Lazarus in Journal of the Institute of Actuaries in 1862. It is a remarkable document.

Our paper on the practical aspects of contemporary mortality modelling for actuaries has was published today by the British Actuarial Journal.  The article is free to access at https://www.doi.org/10.1017/S1357321725000121.  The preprint is also available.

In 1860 William Makeham published a famous paper. In it he extended Gompertz's mortality law to include a constant term:

\[\mu_x=e^\epsilon+e^{\alpha+\beta x}\qquad(1),\]

Today is the 200th anniversary of Benjamin Gompertz's reading of his famous paper before the Royal Society of London.  Generations of actuaries and demographers are familiar with his law of mortality:

\[\mu_x = e^{\alpha+\beta x}\qquad(1),\]

Stephen recently questioned whether the hype around AI models for Life Insurance might be a case of The Emperor's New Clothes. In this blog we discuss an important point of difference: whereas in the fable, a youth reveals the expensive "invisible" new clothes have no substance at all, in our scenario, we find precisely the opposite. AI models utilising machine learning are, far from being see-through, simply not transparent enough.

When we first wrote our survival-modelling software in late 2005, we had to decide how to represent dates for the purpose of calculating exposure times.  We decided to adopt a real-valued approach, e.g. 14th March 1968 would be represented as 1968.177596 (the fractional part is \(\frac{31+29+14}{366}\), since 1968 is a leap year).

In my previous blog I described a real case where so-called artificial intelligence (AI) would have struggled to spot data problems that a (suspicious) human could find.  But what if the input data are clean and reliable?

There is emerging hype about the application of artificial intelligence (AI) to mortality analysis, specifically the use of machine learning via neural networks. In this blog I provide a counter-example that illustrates why the human element is an absolutely indispensable part of actuarial work, and why I think it always will be.

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.

Stephen and I recently presented a pair of papers to the Institute and Faculty of Actuaries: Richards & Macdonald (2024) and Macdonald & Richards (2024).  In these papers we encourage actuaries to use continuous-time models in their work. But where does that leave discrete-time?