Stephen Richards

In a previous blog I demonstrated that there was a statistically significant relationship between pension size and mortality.  In a subsequent blog I looked at the improvements in model fit from treating pension size as a factor, but concluded that this was only a partial solution.  In practice actuaries would prefer to avoid the discretisation error that com

The COVID-19 pandemic has created strong interest in mortality patterns in time, especially mortality shocks. Actuaries now have to consider the effect of such shocks in their portfolio data, and in this blog we consider a non-parametric method of doing this.

It will surprise nobody reading this blog that richer people tend to live longer.  This applies both between countries (countries with a higher per capita income tend to have higher life expectancies) and also within countries (people of higher socio-economic status tend to live longer than others, even when they all share the same comprehensive healthcare system).

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.