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How do you prove something is a martingale?

The useful property of martingales is that we can verify the martingale property locally, by proving either that E[Xt+1|\u2131t] = Xt or equivalently that E[Xt+1 - Xt|\u2131t] = E[Xt+1|\u2131t] - Xt = 0.

Why it is called martingale?

The word martingale came from a group of betting strategies that were popular in France in the 18th century. In a simple game where a gambler wins if a coin comes up heads and loses if it comes up tails (pt = ph = 1/2, assuming a fair coin) the martingale strategy had him double his bet every time he lost.

Is martingale a good strategy?

It is considered a risky method of investing. It is based on the theory of increasing the amount allocated for investments, even if its value is falling, in expectation of a future increase. When the Martingale Strategy is used in betting, the gambler must double the bet when faced with a loss.

What martingale means?

Definition of martingale 1 : a device for steadying a horse's head or checking its upward movement that typically consists of a strap fastened to the girth, passing between the forelegs, and bifurcating to end in two rings through which the reins pass.

What makes something a martingale?

In probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time, the conditional expectation of the next value in the sequence is equal to the present value, regardless of all prior values.

How do you prove something is a martingale?

The useful property of martingales is that we can verify the martingale property locally, by proving either that E[Xt+1|\u2131t] = Xt or equivalently that E[Xt+1 - Xt|\u2131t] = E[Xt+1|\u2131t] - Xt = 0.

Is a random walk a martingale?

Random Walk derives from the martingale theory. The simplest definition of random walk implies that the variation of the variable is also associated with the IID (Independently and Identically Distributed) definition of the distribution of ?t.

How does Martingale make money?

The Martingale system is a simple process that involves doubling your bets after a loss. The idea is that if you can make a bet that offers even odds, or close to even odds, you eventually win and make enough money on the win to cover all of your previous losses, and have a profit left over equal to your first bet.

Why is martingale a fair game?

The martingale condition stipulates that his expected or average fortune after the next play equals his present fortune, and so the martingale is a model for a fair game.

Why is martingale important?

Essentially, the martingale property ensures that in a "fair game", knowledge of the past will be of no use in predicting future winnings. These properties will be of fundamental importance in regard to defining Brownian motion, which will later be used as a model for an asset price path.

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