# What is a martingale in probability?

What is a martingale in probability? 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

## What is a martingale in probability?

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.

## What is the martingale theory?

The Martingale system is a system of investing in which the dollar value of investments continually increases after losses, or the position size increases with the lowering portfolio size. The Martingale system was introduced by French mathematician Paul Pierre Levy in the 18th century.

## Are martingales independent?

Martingales as sums of uncorrelated random variables. , where E[Δi|Δ1…Δi-1] = E[Xi-Xi-1|ℱi] = 0. In other words, Δi is uncorrelated with Δ1…Δi-1. This is not quite as good a condition as independence, but is good enough that martingales often act very much like sums of independent random variables.

## What is the meaning of Submartingale?

submartingale (plural submartingales) (mathematics) A stochastic process for which the conditional expectation of future values given the sequence of all prior values is superior or equal to its current value. If a gambler repeatedly plays a game with positive expectation, his payoff over time is a submartingale.

## Why it is called martingale?

Doob is the one who really made the name popular (in addition to proving many fundamental results). He got the name from a thesis by Ville. A martingale is the name for a Y-shaped strap used in a harness — it runs along the horse’s chest and then splits up the middle to join the saddle.

## What is equivalent martingale measure?

In mathematical finance, a risk-neutral measure (also called an equilibrium measure, or equivalent martingale measure) is a probability measure such that each share price is exactly equal to the discounted expectation of the share price under this measure. The probability measure of a transformed random variable.

## Is the martingale strategy illegal?

The Martingale system is permitted for online casinos. This system is not illegal and nor its use is banned. The Martingale system is known to provide better winning chances. But it also has several restrictions that make its use limited.

## Do martingales have independent increments?

It is true that every continuous martingale X with stationary independent increments is a Brownian motion or, to be precise, X=X0+σBt for a standard Brownian motion B and constant σ. This is because any such process is a Lévy process, and Brownian motions (possibly with drift) are the only continuous Lévy processes.

## Why is martingale important?

The Martingale property states that the future expectation of a stochastic process is equal to the current value, given all known information about the prior events. Both of these properties are extremely important in modeling asset price movements.