Stephen Richards

In a previous post we discussed the possibility of gender being banned throughout the EU as a rating factor for insurance pricing.  This has now come to pass — on 1st March 2011 the European Court of Justice ruled that gender may not be used in insurance pricing according to European law.  So what will happen now?

People in poor health don't live as long as their healthier colleagues. This obvious fact underpins the existence of the enhanced annuity market in the United Kingdom.

Stochastic projection models have many advantages — they not only give best-estimate projections, but also confidence intervals around those projections.

The CMI has released a second version of its deterministic targeting model for mortality improvements. This type of model is called an expectation, as the user must enter their belief for the long-term rate of mortality improvement to use the tool.

Last week we looked at how to compare mortality-improvement bases for pensions and annuities.  However, for many years some pension schemes in the UK did not have explicit mortality-improvement projections.  Instead, they allowed for mortality improvements by making a deduction from the valuation discount rate.

Which mortality-improvement basis is tougher — a medium-cohort projection with a 2% minimum value, or a long-cohort projection with a 1% minimum? Unless you are an actuary who works with such things, you have little chance of answering this question. 

It is often easy to be fooled into thinking that a small change is of little importance.  Small changes can persist over time, and sometimes it is only in retrospect that one realises just how big the accumulated change is.

In actuarial terminology, a mortality "law" is simply a parametric formula used to describe the risk. A major benefit of this is automatic smoothing and in-filling for areas where data is sparse. A common example in modern annuity portfolios is that there is often plenty of data up to age 75 (say), but relatively little data above age 90.

For example, if we use a parametric formula like the Gompertz law:

When fitting mortality models, the foundation of modern statistical inference is the log-likelihood function. The point at which the log-likelihood has its maximum value gives you the maximum-likelihood estimates of your parameters, while the curvature of the log-likelihood tells you about the standard errors of those parameter estimates.

The current issue of The Actuary magazine carries an article on the selection of model points. Model points were widely used by actuaries in the 1980s and 1990s, when computing power was insufficient to perform complex policy calculations on every policy in a reasonable time-frame.