supermartingale
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English
Etymology
super- + martingale
Noun
supermartingale (plural supermartingales)
- (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.