Discrete Stochastic Processes

Martingales for Dummies

The fair game that predicts the future, and why no stopping rule can beat it.

What to remember

  • Martingale = fair game: E[next | now] = now.
  • Optional stopping: E[X_T] = X_0 under boundedness conditions.
  • No betting strategy beats a fair game with finite money.
Read the lessonMartingales and Optional Stopping, with a checkpoint at the end.