Information Matrix

It is fairly obvious by now that we are strong advocates for stochastic projection models. Such models crucially provide a basis with two components - a best-estimate force of mortality by age and year, and matching standard error values for the same 2D range.

A while back I wrote about the lower life expectancy in Scotland. This has a number of drivers, but poor diet is one of them.

I'm giving away rather too much information about my age when I say I started work in 1990 right after graduating from university. Not long into my first job at a UK insurer, I was called to a meeting of the actuarial department.

Longevity trend risk is different from most other risks an insurer faces because the risk lies in the long-term trajectory taken by mortality rates. This trend unfolds over many years as an accumulation of small changes.

If you'll forgive the nautical metaphor, forecasting longevity over the past few decades has proven to be anything but plain sailing. Those plotting a course with unshakable certainty have usually ended up storm-tossed and floating in a barrel.

We and our clients much prefer to analyse mortality continuously, rather than in yearly intervals like actuaries used to do in previous centuries. Actuaries normally use μx to denote the continuous force of mortality at age x, and qx to denote the yearly rate of mortality. For any statisticians reading this, μx is the continuous-time hazard rate.

In an earlier post we looked at the implications for savers of the historically low interest rates in the UK. Low interest rates are a policy response to the unusual economic conditions in which the developed world currently finds itself.

Mortality statistics occasionally make the news, usually with some eye-catching statements.  Here is a recent example from the BBC: "Data from life insurance companies suggests that in the fifth and sixth decades of life you are less likely to die over the coming year than at any other time in your life."

When an insurer or reinsurer takes on a new insurance risk, there are two things of special interest: the best estimate of the risk and the tail risk.