Stephen Richards
Managing Director
Articles written by Stephen Richards
COVID-19 mortality and sex
I recently looked at the progression of Covid-19 mortality risk with age. As with all-cause mortality, another risk factor for Covid-19 is biological sex.
COVID-19 mortality and age
When faced with a pandemic disease, such as the ongoing Covid-19 crisis, a multi-layered approach is useful.
Wash your hands, live longer
As the coronavirus circles the globe, the only thing spreading faster is disinformation on so-called "social media". In addition to ridiculous conspiracy theories, quack preventions range from the ineffective to the downright dangerous.
Best practice in mortality work - regulatory comments
In a letter to the Chief Actuaries of UK insurance businesses, Malik (2019) highlighted two aspects of what the regulator regards as good practice in mortality work
Mortality crossover
In a previous blog I discussed the importance of mortality convergence to actuaries, i.e. how mortality differentials narrow with age and how this interacts with discounting of cashflows.
Model selection
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.
Matrix repair
When fitting a statistical model we want two things as a minimum:
Mortality convergence
In his blog on socio-economic differentials in England and Wales, Torsten Kleinow showed how mortality rates between sub-groups converge with age. And in his blog on ill-health retirements, Kai Kaufhold demonstrated how excess mortality relative to normal retirements reduces, then vanishes.
Seasonal mortality and age
In two previous blogs (here and here) I looked at excess winter mortality. A first glance at the charts shows that the elderly dominate the death counts. However, the elderly also happen to provide the bulk of deaths at any time of year, so how can we be sure that they are more vulnerable to seasonal variation?
The Hermite model of mortality
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:
\[\mu_x = \frac{e^\epsilon+e^{\alpha+\beta x}}{1+e^{\alpha+\rho+\beta x}}\qquad(1)\]