Stephen Richards
Articles written by Stephen Richards
Early retirements
Members of defined-benefit pension schemes can often retire early if they are in poor health. Unsurprisingly, such ill-health retirements exhibit higher mortality rates than those who retire at the normal scheme age.
Accelerating improvements in mortality
In February 2009 a variation on the Lee-Carter model for smoothing and projecting mortality rates was presented to the Faculty of Actuaries. A key question for any projection model is whether the process being modelled is stable. If the process is not stable, then a model assuming it is stable will give misleading projections. Equally, a model which makes projections by placing a greater emphasis on recent data will be better able to identify a change in tempo of the underlying p
Winter mortality
Logistical nightmares
Double trouble
Interesting times
Table talk
Size isn't everything
Great Expectations
When fitting statistical models, a number of features are commonly assumed by users. Chief amongst these assumptions is that the expected number of events according to the model will equal the actual number in the data. This strikes most people as a thoroughly reasonable expectation. Reasonable, but often wrong.
A likely story
The foundation for most modern statistical inference is the log-likelihood function. By maximising the value of this function, we find the maximum-likelihood estimate (MLE) for a given parameter, i.e. the most likely value given the model and data. For models with more than one parameter, we find the set of values which jointly maximise the log-likelihood.