Stephen Richards Profile Picture

Stephen Richards

Managing Director

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.
Tags: Filter information matrix by tag: Scotland, Filter information matrix by tag: region, Filter information matrix by tag: geodemographics

Out for the count

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. 
Tags: Filter information matrix by tag: survival models, Filter information matrix by tag: force of mortality, Filter information matrix by tag: GLM, Filter information matrix by tag: missing data

Stabilising projections

With many stochastic models of mortality, projections of future mortality rates are done using a time seriesIn 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

Tags: Filter information matrix by tag: P-splines, Filter information matrix by tag: time series, Filter information matrix by tag: mortality projections, Filter information matrix by tag: 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. 
Tags: Filter information matrix by tag: buy-out, Filter information matrix by tag: concentration risk, Filter information matrix by tag: trend risk, Filter information matrix by tag: 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.
Tags: Filter information matrix by tag: CMI, Filter information matrix by tag: 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.
Tags: Filter information matrix by tag: obesity, Filter information matrix by tag: 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

Tags: Filter information matrix by tag: basis risk, Filter information matrix by tag: 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.
Tags: Filter information matrix by tag: obesity, Filter information matrix by tag: BMI, Filter information matrix by tag: concentration risk, Filter information matrix by tag: 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.
Tags: Filter information matrix by tag: annuities, Filter information matrix by tag: 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:

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

Tags: Filter information matrix by tag: residual, Filter information matrix by tag: deviance residuals, Filter information matrix by tag: Pearson residuals