Brownian model of financial markets as: Note that formula_21 and formula_139 are absolutely continuous with respect to each other, i.e. they are equivalent. Also, according to Girsanov's theorem, is a formula_6-dimensional Brownian motion process on the filtration formula_146 with respect to formula_139. A complete financial market is one that allows effective hedging of the risk inherent in any investment strategy. Let formula_89 be a standard financial market, and formula_149 be an formula_140-measurable random variable, such that: The market formula_89 is said to be "complete" if every such formula_149 is "financeable", i.e. if there is an formula_155-financed portfolio process formula_156, such that its associated wealth process
Reflected Brownian motion steady state RBMs. Feller described possible boundary condition for the process Reflected Brownian motion In probability theory, reflected Brownian motion (or regulated Brownian motion, both with the acronym RBM) is a Wiener process in a space with reflecting boundaries. RBMs have been shown to describe queueing models experiencing heavy traffic as first proposed by Kingman and proven by Iglehart and Whitt. A "d"–dimensional reflected Brownian motion "Z" is a stochastic process on formula_1 uniquely defined by where "X"("t") is an unconstrained Brownian motion and with "Y"("t") a "d"–dimensional vector where The reflection matrix describes boundary behaviour. In the interior of