In probability theory, the optional stopping theorem (or Doob's optional sampling theorem) says that, under certain conditions, the expected value of a martingale at a stopping time is equal to the expected value of its initial value. Since martingales can be used to model the wealth of a gambler participating in a fair game, the optional stopping theorem says that on the average nothing can be gained by stopping to play the game based on the information obtainable so far (i.e., by not looking into the future). Of course, certain conditions are necessary for this result to hold true, in particular doubling strategies have to be excluded.
The optional stopping theorem is an important tool of mathematical finance in the context of the fundamental theorem of asset pricing.
Read more about Optional Stopping Theorem: Statement of Theorem, Applications, Proof
Famous quotes containing the words optional, stopping and/or theorem:
“Our father presents an optional set of rhythms and responses for us to connect to. As a second home base, he makes it safer to roam. With him as an ally—a love—it is safer, too, to show that we’re mad when we’re mad at our mother. We can hate and not be abandoned, hate and still love.”
—Judith Viorst (20th century)
“Would not some lightning flash of vision sear people’s consciousness into life again? What was the good of stopping the war if armies continued?”
—John Dos Passos (1896–1970)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)