#589 1693 · Edmond Halley / Royal Society · Insurance / actuarial science
Halley priced life annuities correctly by measuring the one variable everyone had been ignoring: age
the problem
Life annuities were sold at one flat price regardless of the buyer's age, because no one had population-level data to price them any other way
background
By the late 1600s, life annuities — a lump sum paid up front in exchange for guaranteed income until the buyer's death — were a common way for governments and institutions to raise money, including cash-strapped states funding wars. But annuities were priced at a single flat rate no matter the buyer's age, because no seller had rigorous population-level mortality data showing how survival odds actually varied across a lifespan.
That flat pricing was a quiet, ongoing loss: a healthy 20-year-old paid the exact same price as a 70-year-old for a product statistically worth many times more to the younger buyer, who could expect decades more of guaranteed payments for the identical upfront cost. Sellers had no way to see the mispricing because they had never measured the thing that would have revealed it — the actual distribution of ages at death across a real population.
what everyone would do
Adjust the price by eye — charge a visibly frail or elderly buyer a little less, haggle case by case — since no rigorous data existed to do anything more precise. It fails because impressions of age and health are unreliable and inconsistent between sellers, and worse, nobody selling this way could even see that systematic mispricing was happening at all: you cannot correct a bias in your pricing that you have no way to measure.
what they saw
Halley saw that the missing ingredient wasn't a smarter pricing formula or sharper judgment about individual buyers, it was population-level data: a real record of how many people from an actual birth cohort were still alive at every subsequent age. Once that survival curve is measured rather than guessed, the fair price at any age follows almost mechanically — the problem had looked like a pricing puzzle for decades because it was actually a data-collection problem no one had solved.
the move
Edmond Halley obtained detailed birth and death records for the city of Breslau, compiled by Caspar Neumann and covering the years 1687 to 1691, and used them to build what is considered the first rigorous, population-based mortality table — showing, for a cohort born in the same year, how many were still alive at every subsequent age. He published the table along with a method for calculating the fair price of a life annuity at any given age in the Royal Society's Philosophical Transactions in 1693.
why it works
Neumann's Breslau records gave Halley real counts of births and deaths across a population over several years, letting him reconstruct exactly how many of an original cohort survived to each later age. That survival distribution directly determines the expected number of future payments an annuity at any given age is really worth, so a fair price could now be calculated rather than assumed. Because price finally tracked true expected value instead of a flat guess, it closed the systematic transfer that had been running from older buyers to younger ones, who had been receiving a far more valuable stream of guaranteed payments for the identical upfront cost.
the payoff
Halley's table made it possible, for the first time, to price a life annuity according to the buyer's actual age-based survival odds rather than a single flat guess applied to everyone, directly correcting the mispricing that had let younger buyers quietly extract far more value than older ones for the same price.
where it breaks
The method depends on a large, representative dataset — Breslau's records were unusually complete for the era, and a thinner or less rigorously kept population produces a noisier table, especially at older ages where fewer surviving cohort members remain to observe. It also assumes the measured population's mortality pattern generalizes to whoever is actually being priced: a table built from one city's disease environment, wealth level, or era misprices a population whose life expectancy differs, which is exactly why actuarial tables require periodic revision rather than permanent reliance on one historical dataset.
what came after
Halley's Breslau table is recognized as the foundational document of actuarial science, and the underlying principle — collecting real population data and pricing risk according to its measured, age-specific distribution rather than a flat average — remains the basis of how life insurance and annuities are priced today, more than 330 years later.
references
- [1]An Estimate of the Degrees of the Mortality of Mankind, drawn from curious Tables of the Births and Funerals at the City of BreslawPhilosophical Transactions of the Royal Society, 1693royalsocietypublishing.org
- [2]Edmond Halley Compiles the Breslau TablesHistory of Information, 2024historyofinformation.com