building a mortality table

A mortality table does not fall from the sky; someone has to build it from data. The task is to take records of who was alive, who died, and over what period, and turn them into a clean set of death rates q-x for each age. This is the bread-and-butter of an experience study, and it is how insurers, pension funds, and statistical agencies learn how their own population actually dies.

The central idea is to estimate each age's death rate as deaths divided by exposure. Deaths are easy to count; the subtlety is exposure — the amount of time lives were actually observed at each age and so genuinely 'at risk'. Someone who joins mid-year, lapses, or turns a year older partway through contributes only a fraction of a year of exposure, and getting this bookkeeping right (central versus initial exposure, handling of new entrants and withdrawals) is most of the craft. A raw rate is then roughly q-x = deaths at age x divided by the exposure at age x.

The raw rates that emerge are bumpy, because at most ages you have only a limited number of deaths and random noise dominates. So a built table is almost never the raw numbers: it is graduated (smoothed) into a sensible progression, tested for goodness of fit, and often split into select and ultimate portions. Good table construction is a careful blend of honest data handling, statistical estimation, and judgement — and a poorly built table quietly poisons every premium and reserve computed from it.