Simple Examples of Martingales

Name some processes that are martingales.

Answer

Examples include:

  • The wealth/profit process in any fair game, i.e., in a game where the expected profit $=0$.

  • Brownian motion $(B_t)_{t \geq 0}$.

  • The simple symmetric random walk (discrete-time analogue of Brownian motion).

  • The discounted asset price process under the risk-neutral measure.

  • The process $M_t = B_t^2 - t$ for Brownian motion $B_t$ (a nontrivial martingale).

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