Stephen Richards

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Articles written by Stephen Richards

Devil in the detail

Last week I wrote about the judgment by the European Court of Justice which bans the use of gender in insurance pricing after 2012. An interesting aspect is the areas of insurance business which may not be affected.

09 March 2011 Tags: gender, annuities

Gender and annuity pricing in the EU

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?

02 March 2011 Tags: gender, annuities

Too good to be true?

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.

22 February 2011 Tags: selection risk, enhanced annuities

Don't shoot the messenger

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

12 February 2011 Tags: mortality projections

Applying the brakes

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. Expectations have their own unique features, as discussed

24 January 2011 Tags: CMI, mortality improvements, mortality projections

Keeping it simple — postscript

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.

17 January 2011 Tags: mortality improvements, mortality projections, equivalent annuity

Keeping it simple

Which mortality-improvement basis is tougher — a medium-cohort projection with a 2% minimum value, or a long-cohort projection with a 1% minimum?

14 January 2011 Tags: mortality improvements, mortality projections, equivalent annuity

The accumulation of small changes

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.

05 January 2011 Tags: mortality improvements, centenarians

Laying down the law

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.

14 December 2010 Tags: log-likelihood, mortality law, CMI, Gompertz-Makeham family

One small step

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.

07 December 2010 Tags: log-likelihood, numerical approximation, derivatives