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Stephen Richards

Managing Director

Articles written by Stephen Richards

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.
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.
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:

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

Factors

In statistical terminology, a factor is a categorisation which contains two or more mutually exclusive values called levels.  These levels may have a natural order, in which case the variable is said to be an ordinal factor. 
Tags: Filter information matrix by tag: factor, Filter information matrix by tag: categorical factor, Filter information matrix by tag: ordinal factor, Filter information matrix by tag: binary factor, Filter information matrix by tag: AIC, Filter information matrix by tag: optimisation

Playing with scales

Mortality rates increase exponentially with age.  This can make comparisons difficult, as shown in Figure 1 below, which shows the period mortality rates for males in England and Wales at ten-year intervals. 
Tags: Filter information matrix by tag: mortality, Filter information matrix by tag: scale