Martingale
A martingale is a process whose conditional expectation of the future, given the present, is the present — ‘fair game’ under that information and that measure.
Definition
Martingale refers to ‘fair game’ under that information and that measure. Keep that definition fixed when comparing series, managers, or regimes — renaming the same tape does not create a new signal.
Why it matters
It is a named object desks use to frame risk, positioning, or process. When ‘fair game’ under that information and that measure shifts, related hedges, limits, and narratives usually need an explicit update rather than a quiet assumption.
Case
Suppose a desk is positioned for the opposite of what martingale is saying. If ‘fair game’ under that information and that measure moves against that book, the first question is not “is the story clever?” but whether size, hedges, and stop logic still match the observation.
How to read it
Keep the definition fixed, then challenge it with cross-checks before sizing. Prefer a short written null hypothesis for Martingale: what would falsify the current reading in the next window?