Halley's table: how was the price of life insurance calculated?

We briefly mentioned the life table in the article "From the life table to the state pension". This time we take a closer look at the table itself: what data it was compiled from, what it shows and how an insurer uses it.

Key points

1. The author. Edmond Halley (1656–1742) was an English astronomer; the comet he predicted is named after him today. In 1685–1693 he also edited the Royal Society's journal "Philosophical Transactions" (Encyclopedia.com).
2. The article. In 1693 Halley's article appeared in volume 17 of this journal (pp. 596–610). Its title runs roughly as follows: "An estimate of the degrees of the mortality of mankind, drawn from curious tables of the births and funerals at the city of Breslaw; with an attempt to ascertain the price of annuities upon lives".
3. The source of data. Halley used the birth and burial records of the city of Breslau (today's Wrocław in Poland). These records were collected by Caspar Neumann, a clergyman from Breslau, and sent to the Royal Society.
4. Why Breslau? As Halley explains in his article, London and Dublin had many incomers from outside, which would distort the calculation; in Breslau the number of births was slightly higher than the number of burials, so he considered the population of this city the most suitable as a "standard". In today's statistical language: reducing the factors that distort the observation.
5. What does the table give? The table shows how many of those born in one year remain alive up to each age. From this one can calculate how many people of a given age will be alive a year later.
6. Calculating the price. According to a study in the actuaries' journal, Halley used the table to calculate the price of life annuities tied to one, two and three lives. This was one of the first scientific examples of turning the assumption "who will live how long" into money.
7. He was not alone. It should not be forgotten that people worked with mortality data before Halley: John Graunt's work on the London Bills of Mortality is a striking example; the historian of actuaries C. Lewin also notes that there were one or two similar works before Halley, but stresses that the influential work that started actuarial science was Halley's.

Example: reading a life table

Suppose the hypothetical insurance company "Umr Kafolat" is calculating the price of one-year life insurance. The simplified table it has looks like this (compiled by the author, hypothetical figures, not real statistics):

If the sum insured is 100 000 000 soum, the "net" premium needed to cover the risk comes out approximately as follows:

• for Botir aged 40: 100 000 000 × 0.3% = 300 000 soum;
• for Botir aged 50: 100 000 000 × 0.6% = 600 000 soum;
• for Botir aged 60: 100 000 000 × 1.5% = 1 500 000 soum.

The actual premium will be higher, because the company's expenses, reserves and profit are added to it, and the time value of money is also taken into account. But the heart of the calculation is the same: assessing the risk of one person from data about many people. Halley showed exactly this path in 1693.