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)
“I still think I ought to leave Washington well alone. I have many friends in that city who can of their own motion speak confidently of my ways of thinking and acting. An authorized representative could remove some troubles that you now see, but only think of yet greater troubles he might create.”
—Rutherford Birchard Hayes (1822–1893)