#32 1693 · Edmond Halley / Royal Society · Insurance / actuarial sciencelegibility
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.
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.
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.
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.
filed under
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