Consider a stochastic process \(X = (X_t, 0 \le t \le 1)\). A familiar theorem states (in contrapositive form, and ignoring technical conditions)
\(X\) is not a martingale if and only if there exists a stopping time \(T\) such that \(EX_T \neq EX_0\).
I would like to define a class of processes, say "martingale for practical purposes" (MPP) by
Problem. Make sense of this definition.
This arises from the efficient market hypothesis, which is usually taken to imply short-term prices should follow a martingale, but really implies they should follow some MPP.