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Geometric Brownian Motion
A geometric Brownian motion (GBM) (also known as exponential Brownian motion) is a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion (also called a Wiener process) with drift. It is an important example of stochastic processes satisfying a stochastic differential equation (SDE); in particular, it is used in mathematical finance to model stock prices in the Black–Scholes model. Technical definition: the SDE A stochastic process ''S''''t'' is said to follow a GBM if it satisfies the following stochastic differential equation (SDE): : dS_t = \mu S_t\,dt + \sigma S_t\,dW_t where W_t is a Wiener process or Brownian motion, and \mu ('the percentage drift') and \sigma ('the percentage volatility') are constants. The former parameter is used to model deterministic trends, while the latter parameter models unpredictable events occurring during the motion. Solving the SDE For an arbitrary initial value '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GBM2
GBM may refer to: Medicine * ''Glioblastoma multiforme'', an outdated term for glioblastoma * Glomerular basement membrane Science and technology * Gateway belief model, a model in psychology and the communication sciences * Geometric Brownian motion, continuous stochastic process where the logarithm of a variable follows a Brownian movement, that is a Wiener process * Gradient boosting, a machine learning technique * Generic Buffer Management, a graphics API * Gamma-ray Burst Monitor, aboard the Fermi Gamma-ray Space Telescope * Game Boy Micro, a 2005 handheld game console and the last model in the Game Boy line Other uses * Grand Besançon Métropole, a French intercommunal structure * GBM (''League of Legends'' player) (born 1994), Korean video gamer * Geoffrey Bwalya Mwamba (born 1959), Zambian politician * Garbaharey Airport, in Somalia * Garhwali language * Grand Bauhinia Medal The Grand Bauhinia Medal () is the highest award under the Decorations and medals of Hon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variance
In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. It is the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by \sigma^2, s^2, \operatorname(X), V(X), or \mathbb(X). An advantage of variance as a measure of dispersion is that it is more amenable to algebraic manipulation than other measures of dispersion such as the expected absolute deviation; for example, the variance of a sum of uncorrelated random variables is equal to the sum of their variances. A disadvantage of the variance for practical applications is that, unlike the standard deviation, its units differ from the random variable, which is why the standard devi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
