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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. Stopped Brownian motion is an example of a martingale. It can model an even coin-toss ...
The software runs on Windows 98/2000/XP/Vista/7. Some users have reported success using Wine on Linux for the client terminal [22] and on Mac using WineBottler. [23] MetaTrader 4 Mobile - controls a trading account via mobile devices such as mobile phones or PDAs. Runs on Windows Pocket PC 2002/Mobile 2003, [24] iOS, [25] and Android. [26]
A martingale is a class of betting strategies that originated from and were popular in 18th-century France. The simplest of these strategies was designed for a game in which the gambler wins the stake if a coin comes up heads and loses if it comes up tails.
If in a financial market there is just one risk-neutral measure, then there is a unique arbitrage-free price for each asset in the market. This is the fundamental theorem of arbitrage-free pricing . If there are more such measures, then in an interval of prices no arbitrage is possible.
A discrete-time version of the theorem is given below, with 0 denoting the set of natural integers, including zero.. Let X = (X t) t∈ 0 be a discrete-time martingale and τ a stopping time with values in 0 ∪ {∞}, both with respect to a filtration (F t) t∈ 0.
In the mathematical theory of probability, a Doob martingale (named after Joseph L. Doob, [1] also known as a Levy martingale) is a stochastic process that approximates a given random variable and has the martingale property with respect to the given filtration. It may be thought of as the evolving sequence of best approximations to the random ...
Martingale pricing is a pricing approach based on the notions of martingale and risk neutrality. The martingale pricing approach is a cornerstone of modern quantitative finance and can be applied to a variety of derivatives contracts, e.g. options , futures , interest rate derivatives , credit derivatives , etc.
By construction, this implies that if is a martingale, then = will be an MDS—hence the name. The MDS is an extremely useful construct in modern probability theory because it implies much milder restrictions on the memory of the sequence than independence , yet most limit theorems that hold for an independent sequence will also hold for an MDS.