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On the Integral of Gompertz's Function for expressing the Values of Sums depending upon the contingency of life

1873; Cambridge University Press; Volume: 17; Issue: 5 Linguagem: Inglês

10.1017/s2046167400044268

2396-8249

William Matthew Makeham,

Risk and Portfolio Optimization

Gompertz's Function for expressing the probability of a person surviving any given period, x , is . For the purpose of adapting this expression to the entire period of adult life I have added the factor ∈ − ax . The two expressions become identical in form when the factor ∈ −δ x representing the effect of discount is introduced, and both may therefore be correctly designated by the name of “Gompertz's Function.”