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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.
Tags: Filter information matrix by tag: coronavirus, Filter information matrix by tag: mortality

COVID-19 mortality and age

When faced with a pandemic disease, such as the ongoing Covid-19 crisis, a multi-layered approach is useful.
Tags: Filter information matrix by tag: coronavirus, Filter information matrix by tag: mortality

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.
Tags: Filter information matrix by tag: coronavirus, Filter information matrix by tag: influenza, Filter information matrix by tag: hygiene

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
Tags: Filter information matrix by tag: season, Filter information matrix by tag: mortality improvements, Filter information matrix by tag: cohort effect

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.
Tags: Filter information matrix by tag: mortality convergence, Filter information matrix by tag: crossover

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.

Tags: Filter information matrix by tag: information criterion, Filter information matrix by tag: AIC, Filter information matrix by tag: relative likelihood

Matrix repair

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

Tags: Filter information matrix by tag: information matrix, Filter information matrix by tag: covariance matrix

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.
Tags: Filter information matrix by tag: mortality convergence, Filter information matrix by tag: compensation law of mortality, Filter information matrix by tag: mortality plasticity

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?
Tags: Filter information matrix by tag: season, Filter information matrix by tag: winter

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:

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

Tags: Filter information matrix by tag: Hermite splines, Filter information matrix by tag: extrapolation