Probability theory in stock market
In probability theorya martingale is a sequence of random variables i. To contrast, in a process that is not a martingale, it may still be the case that the expected value of the process at one time is equal to the expected value of the process at the next time. However, knowledge of the prior outcomes e. Thus, the expected value of the next outcome given knowledge of the present and all prior outcomes may be higher than the current outcome if a winning strategy is used.
Martingales exclude the possibility of winning strategies based on game history, and thus they are a model of fair games.
Originally, martingale referred to a class of betting strategies that was popular in 18th-century France. The strategy had the gambler double his bet after every loss so that the first win would recover all previous losses plus win a profit equal to the original stake.
As the gambler's wealth and available time jointly approach infinity, his probability of eventually flipping heads approaches 1, which makes the martingale betting strategy seem like a sure thing.
However, the exponential growth of the bets eventually bankrupts its users, assuming the obvious and realistic finite bankrolls one of the reasons casinosthough normatively enjoying a mathematical edge in the games offered to their patrons, impose betting limits. Stopped Brownian motionwhich is a martingale process, can be used to model the trajectory of such games. Much of the original development of the theory was done by Joseph Leo Doob among others.
Part of the motivation for that work was to show the impossibility of successful betting strategies. A basic definition of a discrete-time martingale is a discrete-time stochastic process i.
That is, the conditional expected value of the next observation, given all the past observations, is equal to the most recent observation. Similarly, a continuous-time martingale with respect to the stochastic process X t is a stochastic process Y t such that for all t.
In full generality, a stochastic process Y: It is important to note that the cara investasi di forex of being a martingale involves both the filtration and the probability measure with respect to which the expectations are taken.
These definitions reflect a relationship between martingale theory and potential theorywhich is the study singapore forex trading account harmonic functions. Given a Brownian motion process W t and a harmonic function fthe resulting process f W t is also a martingale.
The intuition behind the definition is that at any particular time tyou can look at the sequence so far and tell if it is time to stop. An example in real life might be the time at which a gambler leaves the gambling table, which might be a function of his previous winnings for example, free forex signals forum might leave only when he goes brokebut he can't choose to go or stay based on the outcome of games that haven't been played yet.
That is day strategies tool trading breakout weaker condition than the one appearing in the paragraph above, but is strong enough to serve in some of the proofs in which stopping times are used. The concept of binary options safe martingale strategy stopped martingale leads to a series of important theorems, including, for example, the optional stopping theorem which states that, under certain conditions, the expected value of a martingale at a stopping time probability theory in stock market equal to its initial value.
From Wikipedia, the free encyclopedia. For the martingale betting strategy, see martingale betting system. Azuma's inequality Brownian motion Martingale central limit theorem Martingale representation theorem Doob martingale Doob's martingale convergence theorems Local martingale Semimartingale Martingale difference sequence Markov chain Martingale betting system.
Money Management Strategies for Futures Traders. Electronic Journal for History of Probability and Statistics. Probability and Random Processes 3rd ed. Bernoulli process Branching process Chinese restaurant process Galton—Watson process Independent and identically distributed random variables Markov chain Moran process Random walk Loop-erased Self-avoiding Biased Maximal entropy.
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