Another look at the Gompertz model

(Mar 28, 2020)

The year 1825 was a significant one not only for actuaries but for the wider scientific community: Benjamin Gompertz published his landmark paper on the graduation of human mortality (Gompertz, 1825).  There were at least three completely new ideas in his paper.  First, he gave his famous law of mortality.  To quote Gompertz:

"at the age \(x\) the intensity of man's mortality might be denoted by \(aq^x\)"

or put another way, the logarithm of the force of mortality is linear in age.  Second, the data he used was very limited and was available only at ten-year intervals; his law enabled him to interpolate between these given ages.  Third, and this was significant for actuaries, he had a new way of valuing life contingencies.

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