Stephen Richards

Everyone is familiar with the idea of a forecast. You have data on a phenomenon up to the current time, and want to forecast the phenomenon at some point in the future.  The most obvious example is the weather forecast, but forecasting is also required in pension and annuity work.  For example, when calculating reserves for pension payments, some kind of projection is required for future mortality improvements.

The title of this blog is the opening of A Visit from St.

A spline is a mathematical function.  They are used wherever flexibility and smoothness are required, from computer-aided design and cartoon graphics, to the graduation of mortality tables (McCutcheon, 1974).  There are numerous different types of spline, but the most common is the spline proposed by Schoenberg (1964).  Figure 1 shows Schoenberg splines of degrees 0–3, all of which start in 2015:

In an earlier blog I quoted extensively from "The Mythical Man-Month", a book by the distinguished software engineer Fred Brooks.  My blog was admittedly self-interested(!) when it cited arguments made by Brooks (and others) for when it makes sense to buy software instead of writing it yourself.  However in place of "buying

I'm not a fan of the hyperbolic use of military metaphors in civilian life.  However, in rare cases they do seem appropriate, and the ongoing SAR-Cov-2 pandemic provides an example.  After all, describing a worker as "front-line" seems justified when the occupation carries a materially increased risk of infection and death (SAGE, 2021).

The ongoing coronavirus pandemic has so far produced two mortality shocks in the UK and many other countries.  Unsurprisingly, the extra mortality is also visible in annuity portfolios.  Such mortality spikes create a c

If you are in the business of pricing and managing longevity risk, you need software to help you perform your analysis. You have two choices: