Life Annuity - History

History

The instrument's evolution has been long and continues as part of actuarial science. Medieval German and Dutch cities and monasteries raised money by the sale of life annuities, and it was recognized that pricing them was difficult. The early practice for selling this instrument did not consider the age of the nominee, thereby raising interesting concerns. These concerns got the attention of several prominent mathematicians over the years, such as Huygens, Bernoulli, de Moivre and others: even Gauss and Laplace had an interest in matters pertaining to this instrument. It seems that Johan de Witt was the first writer to compute the value of a life annuity as the sum of expected discounted future payments, while Halley used the first mortality table drawn from experience for that calculation. Meanwhile, the Paris Hôtel-Dieu offered some fairly priced annuities that roughly fit the Deparcieux table discounted at 5%. Here is a quick comparison table of early life annuity prices:

Head age (x) Value of a unit annuity
Ulpian

ca. 200 AD

de Witt

1671

Hôtel Dieu

ca. 1680

Halley

1693

Deparcieux

1746

1 30 16 n/a 10,28 n/a
10 30 15,19 n/a 13,44 16,25
20 28 13,83 20 12,78 15,58
30 22 12,22 20 11,72 14,84
40 19 10,39 15 10,57 13,62
50 9 8,68 12 9,21 11,58
60 5 6,70 10 7,60 9,24
70 5 3,77 8 5,32 6,36
80 5 0 8 3,05 3,86
90 5 0 6 1,74 1,58
95 5 0 n/a 1,02 0
Values are approximated

Continuing practice is an everyday occurrence with well-known theory founded on robust mathematics, as witnessed by the hundreds of millions worldwide who receive regular remuneration via pension or the like. The modern approach to resolving the difficult problems related to a larger scope for this instrument applies many advanced mathematical approaches, such as stochastic methods, game theory, and other tools of financial mathematics.

Read more about this topic:  Life Annuity

Famous quotes containing the word history:

    You treat world history as a mathematician does mathematics, in which nothing but laws and formulas exist, no reality, no good and evil, no time, no yesterday, no tomorrow, nothing but an eternal, shallow, mathematical present.
    Hermann Hesse (1877–1962)

    I believe that history has shape, order, and meaning; that exceptional men, as much as economic forces, produce change; and that passé abstractions like beauty, nobility, and greatness have a shifting but continuing validity.
    Camille Paglia (b. 1947)

    The second day of July 1776, will be the most memorable epoch in the history of America. I am apt to believe that it will be celebrated by succeeding generations as the great anniversary festival. It ought to be commemorated, as the day of deliverance, by solemn acts of devotion to God Almighty. It ought to be solemnized with pomp and parade, with shows, games, sports, guns, bells, bonfires and illuminations, from one end of this continent to the other, from this time forward forever more
    John Adams (1735–1826)