Information Matrix

In the first of a pair of blogs we will look at how to allow for changes in mortality levels when calibrating models to experience analysis.  We start with time-varying extensions of traditional parametric models proposed by actuaries, beginning of course with the Gompertz (1825) model:

\[{\rm Gompertz}: \mu_{x,y} = e^{\alpha+\beta x + \delta(y-2000)}\qquad (1)\]

In my previous blog I looked at the implied mortality improvements from time-varying traditional actuarial survival models.  In this blog we consider the implied improvements under the newer Hermite-spline model I proposed in Richards (2019).  This paper included an explicit attempt to model age-related mortality changes, as dis

When underwriting a pension scheme for a bulk annuity or longevity swap, the first concern is understanding what mortality levels are, especially differentials amongst sub-groups. The next concern is whether the recent mortality improvements in the pension scheme are in line with the pricing basis; if the scheme has experienced faster improvements, say, then this would be a valuable insight for pricing.

The importance of seasonal analysis was underscored by a recent letter form the UK insurance regulator. In a previous blog, I looked at quarterly seasonal variation in a portfolio of defined-benefit pensions, and in a more recent blog I looked at monthly seasonal variation in mortality in England & Wales.