Every year is a hurdle. How far the cohort gets is what you owe.
You sold this annuity. Now find out what you actually owe.
A cohort aged 65 collects 20,000 a year for up to 20 years. Each year is a hurdle, and the hurdles get taller as mortality rises. How far the runner gets is the survival curve - and what you owe is that curve, discounted.
q ₓ / p ₓone year at a time
ₖp ₓsurvival compounds
DISCOUNTINGtime and mortality
LONGEVITY RISKliving longer costs you
Interview lens: an annuity writer is short longevity. Every improvement in mortality - every good news story about medicine - makes this liability bigger.