Defined terms for the annuity market and lifetime income landscape.
A non-ergodic system is a system in which the time average and the ensemble average of an outcome differ — the average outcome experienced by a single agent over time is not equal to the average outcome across many agents at a single moment.
Path dependency is the property of a system in which the outcome at any point depends on the specific sequence of events that produced it, not merely on the total amount or distribution of those events.
Risk sharing in the ergodicity context is the mechanism, identified in Ole Peters' ergodicity economics, by which agents who would each face a non-ergodic outcome alone pool their realized outcomes so that each member's time-average experience converges on the ensemble average.
Ruin probability is the chance that a process crosses an absorbing barrier — typically zero wealth in financial contexts — within a specified time horizon.
The St. Petersburg paradox is Daniel Bernoulli's 1738 problem: a hypothetical gamble with infinite expected value that no reasonable person would pay much to play, used historically as a foundational case for distinguishing expected value from optimal decision-making.
