Angus Macdonald

I rediscovered my Faculty of Actuaries diploma recently, having misplaced it in a house move some years ago. It testifies to my knowledge of ‘the doctrine of probabilities’, which is nice. But not long after I received it, Prof Hans Bühlmann classified actuaries like me as ‘Actuaries of the First Kind’ and said:

Contrary to [the Actuary] of the First Kind in life assurance, whose methods were essentially deterministic, [the Actuary of the Second Kind] had to master the skills of probabilistic thinking.

Stephen and our late and much-missed colleague Iain Currie each once marked the presentation of a paper to a sessional meeting of the IFoA by penning some verse for the dinner that followed.  The recent presentation of Macdonald & Richards (2024) therefore provided my excuse for the following lines.

Look in any good bookshop (or on Amazon) and you will find any number of books describing the spectacular failures of financial institutions.

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?

I must have been one of many students who chose maths over medicine, because I have a terrible memory, and medics have to memorize books by the kilogram. In maths, if you understand how to do something, there is nothing to remember.  Right?

Up to a point.  Here are three mathematical relations where the order or direction matters, that I can never remember, no matter how often I have encountered them.

You are in charge of systems programming for an insurer writing disability insurance.  It is your job to write reporting modules to meet the needs of the actuaries, claims managers, accountants and so on.  Where to start?

The data would seem to be a good place.  I'll take it as read what kind of data the business will generate.  The question is how to represent it for efficient use in our programs - something we worry about so that the user doesn't have to.

In the course of a recent investigation, with my colleagues Dr Oytun Haçarız and Professor Torsten Kleinow, a key parameter was the mortality rate of persons suffering from Hypertrophic Cardiomyopathy (HCM), an inherited heart disorder characterized by thickening of the left ventricular muscle wall.  It is quite rare, so precision is not to be expected, and indeed an annual mortality rate of 1% \((q_x=0.01)\), independent of age \(x\), is widely cited.  I

In his recent blog Stephen described some empirical evidence in support of his practice of discarding the most recent six months' data, to reduce the effect of delays in reporting deaths. This blog demonstrates that the practice can also be justified theoretically in the survival modelling framework, although the choice of six months as the cut-off remains an empirical matter.