Stephen Richards

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Articles written by Stephen Richards

A Scottish question

The Scots are an innovative bunch, including the inventor of the telephone and the discoverer of penicillin.

02 September 2009 Tags: Scotland, region, geodemographics

In an earlier post we described a problem when fitting GLMs for qx over multiple years. The key mistake is to divide up the period over which the individual was observed in a model for individual mortality.

31 July 2009 Tags: survival models, force of mortality, GLM, missing data

Stabilising projections

With many stochastic models of mortality, projections of future mortality rates are done using a time series. In a landmark paper, Currie, Durban and Eilers (2004) introduced the idea of using P-splines as an alternative means of generating a forecast. P-splines formed the basis of a projection tool the CMI made fr

21 July 2009 Tags: P-splines, time series, mortality projections, CMI

Partial buy-outs

It is quite common for a pension scheme to want to reduce its risk, but to be unable to afford a full buy-out. The question is how best to reduce risk with the funds available, i.e. which liabilities to buy out first.

14 July 2009 Tags: buy-out, concentration risk, trend risk, tail risk

Expectations v. extrapolations

The CMI has published two working papers along with its new mortality projection model. The proposed new model blends current improvement rates into an expected long-term average rate of improvement. The hope is that such models can incorporate expert opinions on mortality trends to improve the accuracy of projections.

09 July 2009 Tags: CMI, mortality projections

Discrimination

In an earlier blog I discussed the role of Body-Mass Index (BMI) in measuring obesity. An alternative measure to the BMI is to measure your waistline, since this is more directly indicative of health-threatening abdominal fat than the BMI is.

08 July 2009 Tags: obesity, discrimination

Self-selection

Actuaries valuing pension liabilities need to make projections of future mortality rates. The future is inherently uncertain, so it is best to use stochastic models of mortality. Unfortunately, such models require a long enough time series, but few (if any) portfolios have such data. In the UK actuaries typically rely on one of two alternative data sets: the England & Wales data from the ONS, which goes back to 1961, or the "assured lives" data from the CMI, wh

03 July 2009 Tags: basis risk, CMI

Measuring obesity

Obesity is a public-health concern throughout the developed world, since it is linked to a variety of chronic conditions such as diabetes.

23 June 2009 Tags: obesity, BMI, concentration risk, basis risk

Are annuities expensive enough?

The rationale of any business is to make a profit. This is usually achieved by selling things for more than they cost to make or supply.

08 June 2009 Tags: annuities, profit

Residual concerns

One of the most important means of checking a model's fit is to look at the residuals, i.e. the standardised differences between the actual data observed and what the model predicts. One common definition, known as the Pearson residual, is as follows:

\[r = \frac{D-E}{\sqrt{E}}\qquad(1)\]

05 June 2009 Tags: residual, deviance residuals, Pearson residuals