Information Matrix

While researching my paper on the actuarial origins of survival models (Richards, 2026), I had cause to re-read Gompertz (1825).  Strictly speaking I should say "re-try", as my first attempt to read his paper as an undergraduate failed.  Part of the reason for this was notation that was incomprehensible to me in the late 1980s.  Figure 1 shows an example:

Figure 1. Expression from Gompertz (1825, p.539).

The sooner you know about a problem, the sooner you can do something about it.  I have written before about real-time updates to mortality estimates during shocks.  However, real-time methods also have application to everyday management questions.  Consider Figure 1(a), which shows a surge in new annuities in December 2014.  The volume of new annuities written in that month was large enough to shift the average age of the in-force annuit

Actuarial work involves calculating the present value of future liabilities.  In the case of pension funds and annuity portfolios, this means valuing future pension payments. This typically involves calculating a lot of annuity factors, often using spreadsheets.