Stephen Richards
Managing Director
Articles written by Stephen Richards
From small steps to big results
In survival-model work there is a fundamental relationship between the \(t\)-year survival probability from age \(x\), \({}_tp_x\), and the force of mortality, \(\mu_x\):
\[{}_tp_x = \exp\left(-\int_0^t\mu_{x+s}ds\right).\qquad(1)\]
Risk transfer...and transfer risk
The risk-transfer market for defined-benefit pensions in the UK has been buoyant for many years. There is considerable demand from pension schemes — to say nothing of their sponsoring employers — for solutions that transfer risks to insurers.
Age rating
Back in the days before personal computers, actuaries relied solely on published tables for their calculations. These were not just the mortality tables, but monetary functions of these tables known as commutation factors. My old student tables from 1980 list commutation and other factors at discount rates of 4%, 6% and 8% (the latter rate seems almost comically high by current standards).
How much data do you need?
There are two common scenarios when an actuary has to come up with a mortality basis for pensioners or annuitants.
Twin peaks
If you are over forty, the title of this blog will call to mind an iconic, sometimes disturbing, television series of the same name from 1990. If you clicked on the link expecting murder, surreal horror and an undercurrent of sleaze, however, then this posting is as far away from all that as you are ever likely to get.
Fifty years of mortality improvements
In an earlier post we looked at the development of the distribution of age at death over time. We saw how the peak adult age at death had continuously moved towards an ever-higher age.
Changing patterns of mortality
In an earlier post we introduced the idea of the so-called curve of deaths, which is simply the distribution of age at death. This is intimately bound up with survival models and the idea of future lifetime as a random variable.
On the (funding) level
When I read Allan Martin's earlier blog on how pension-scheme reserves routinely fail to include expenses, I was so surprised I had to ask him if it was really true. As a former life-insurance actuary, any reserve which didn't include an allowance for expenses simply wasn't a complete assessment of the liability in my view.
The alias problem
A problem that can crop up during mortality modelling is that of aliasing, specifically extrinsic aliasing. The situation can be illustrated by an example of the sort of data available for a pension scheme.
Division of labour
At this time of year insurers have commenced their annual valuation of liabilities, part of which involves setting a mortality basis. When doing so it is common for actuaries to separate the basis into two components.