Stephen Richards

When fitting a mortality model, analysts are faced with the decision of which risk factors to include or exclude.  One way of doing this is to look for the improvement in an information criterion that balances the fit against the number of parameters.  The bigger the improvement in the information criterion, the more strongly the model with the smaller value is preferred.

When fitting a statistical model we want two things as a minimum:

In Richards (2012) I compared seventeen different parametric models for modelling the mortality of a portfolio of UK annuitants. The best-fitting model, i.e. the one with the lowest AIC, was the Makeham-Beard model:

\[\mu_x = \frac{e^\epsilon+e^{\alpha+\beta x}}{1+e^{\alpha+\rho+\beta x}}\qquad(1)\]

Mortality at post-retirement ages has three apparent stages:

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