Page "Johan de Witt" Paragraph 20

In 1671 De Witt conceived of a life annuity as a weighted average of annuities certain where the weights were mortality probabilities ( that sum to one ), thereby producing the expected value of the present value of a life annuity.

Edmond Halley ’ s ( of comet fame ) representation of the life annuity dates to 1693, when he re-expressed a life annuity as the discounted value of each annual payment multiplied by the probability of surviving long enough to receive the payment and summed until there are no survivors.

De Witt's approach was especially insightful and ahead of its time.

In modern terminology, De Witt treats a life annuity as a random variable and its expected value is what we call the value of a life annuity.

Also in modern terminology, De Witt's approach allows one to readily understand other properties of this random variable such as its standard deviation, skewness, kurtosis, or any other characteristic of interest.