The factors that determine activity on the Exchange are innumerable, with events, current or expected, often bearing no apparent relation to price variation. Beside the somewhat natural causes for variation come artificial causes: The Exchange reacts to itself, and the current trading is a function, not only of prior trading, but also of its relationship to the rest of the market. The determination of this activity depends on an infinite number of factors: It is thus impossible to hope for mathematical forecasting. Contradictory opinion about these variations are so evenly divided that at the same instant buyers expect a rise and sellers expect a fall.
The calculus of probability can doubtless never be applied to market activity, and the dynamics of the Exchange will never be an exact science. But it is possible to study mathematically the state of the market at a given instant—that is to say, to establish the laws of probability for price variation that the market at that instant dictates. If the market, in effect, does not predict in fluctuations, it does assess them as being more or less likely, and this likelihood can be evaluated mathematically.
That’s from the opening lines of “Theorie de la Spéculation” by 20th century French Mathematician Louis Bachalier (1870-1946). Mr Bachalier has been credited with being the first person to model the stochastic process now called Brownian motion, which was part of his PhD thesis The Theory of Speculation, (published 1900). [Wikipedia.org]
Source: Benoit B. Mandelbrot and Richard L. Hudson, The (Mis) Behaviour of Markets p.51
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