Continuous improvement

(Oct 12, 2020)

In a previous blog I demonstrated that there was a statistically significant relationship between pension size and mortality.  In a subsequent blog I looked at the improvements in model fit from treating pension size as a factor, but concluded that this was only a partial solution.  In practice actuaries would prefer to avoid the discretisation error that comes with treating a real-valued variate as a discrete factor.  Furthermore, it would be useful for pricing bases if a pension-size mortality effect could be extrapolated to values beyond those in the calibrating data set.

The first hurdle in modelling mortality continuously by pension size is the presence of extreme values in actuarial data sets. This…

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Tags: discretisation error, transform function, response function

Pension size as a factor

(Oct 6, 2020)

In a previous blog I showed that there was often a statistically significant link between pension size and mortality.  It is clearly necessary to account for such a link in an actuarial mortality model, not least because people with larger pensions account for a disproportionate share of portfolio risk.

Pension size is essentially a continuous covariate, and a simple approach is to discretise, i.e. create non-overlapping ranges.  We sort the pensions within a portfolio, then define break-points such that equal numbers of lives fall into each band (or as close to equal as we can achieve).  Each life can then be assigned a size-band as a risk factor in the same way that they can have a gender; the only difference…

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Tags: discretisation error

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