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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?
Written by: Stephen RichardsTags: gender, annuities

Forecasting mortality at high ages

The forecasting of future mortality at high ages presents additional challenges to the actuary. As an illustration of the problem, let us consider the CMI assured-lives data set for years 1950–2005 and ages 40–100 (see Stephen's blog posts on selection and data volumes). The blue curve (partly hidden under the green curve) in Figure 1 shows observed log(mortality) averaged over time.

Written by: Iain CurrieTags: missing data, mortality projections, age extrapolation

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.
Written by: Stephen RichardsTags: 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.
Written by: Stephen RichardsTags: 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

Written by: Stephen RichardsTags: 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.
Written by: Stephen RichardsTags: 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?

Written by: Stephen RichardsTags: 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.
Written by: Stephen RichardsTags: 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.

Written by: Stephen RichardsTags: 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.
Written by: Stephen RichardsTags: log-likelihood, numerical approximation, derivatives