April 8th, 2007, 2:36 pm
Let Wt be the process of the stock price, then for example the up-move of the stock price doesn't depend on the value of the stock at time t. It also allows for another handy property - markov property of brownian motion. For example, the process W(t+a) - W(a) for a constant a is brownian motion - so, generally it's related to market efficiency - all the info is in the price so future price behavior isn't dependent on the past prices.As for W(t1), it is independent of every (W(t3) - W(t2)) where (0,t) and (t2,t3) don't overlap.I don't really know - the point in mathematics is to build the simplest possible model with good approximation, the brownian motion seems to fit, and independent increments are a big plus
Last edited by
Zedr0n on April 7th, 2007, 10:00 pm, edited 1 time in total.