supermartingale

English

Etymology

super- +‎ martingale

Noun

supermartingale (plural supermartingales)

1. (mathematics) A stochastic process for which the conditional expectation of future values given the sequence of all prior values is bounded above by the current value.

   If a gambler repeatedly plays a game with negative expectation, his payoff over time is a supermartingale.

   • 2018, Lars Ljungqvist and Thomas J. Sargent, Recursive macroeconomic theory, 4th edition, MIT Press, page 6:

     With these assumptions, something amazing occurs: Euler inequality (1.3.3) implies that the marginal utility of consumption is a nonnegative supermartingale. [emphasis in original]

Usage notes

A supermartingale is a martingale if and only if it is also a submartingale.