The Long Shadow of the Life Table

(Oct 27, 2018)

For centuries, the life table has been at the centre of actuarial work.  It sets out the gradual extinction of a hypothetical population, often a birth cohort.  At age \(x\), \(l_x\) individuals are still alive, and \(d_x\) of them die during the next year, so in a year's time \(l_{x+1} = l_x - d_x\) are still alive, and so on.  The following table is an extract from a life table, describing 100,000 persons in a birth cohort, of whom the last dies age 114.

Age \(x\) \(l_x\) \(d_x\)
0 100,000 362
1 99,638 236
2 99,402 225
3 99,177 229
4 98,948 234
\(\ldots\) \(\ldots\) \(\ldots\)
\(\ldots\) \(\ldots\) \(\ldots\)
111 18 10
112 8 5
113 3 2
114 1 1
115 0  

The life table is simple, intuitive, and requires hardly any mathematics to…

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