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.
Read more about Geometric Brownian Motion: Technical Definition: The SDE, Solving The SDE, Properties of GBM, Multivariate Geometric Brownian Motion, Use of GBM in Finance, Extensions of GBM
Famous quotes containing the words geometric and/or motion:
“New York ... is a city of geometric heights, a petrified desert of grids and lattices, an inferno of greenish abstraction under a flat sky, a real Metropolis from which man is absent by his very accumulation.”
—Roland Barthes (1915–1980)
“Happier of happy though I be, like them
I cannot take possession of the sky,
Mount with a thoughtless impulse, and wheel there,
One of a mighty multitude whose way
And motion is a harmony and dance
Magnificent.”
—William Wordsworth (1770–1850)