Publication Year

1996

Keywords

Mathematics, stock market, Brownian motion, economics

Disciplines

Economics | Mathematics | Physical Sciences and Mathematics

Abstract

Brownian motion arose (1827) in an attempt to explain the motion exhibited by small particles totally immersed in a liquid or gas. The phenomenon of Brownian motion was discovered by the English botanist Robert Brown. The first explanation of Brownian motion was given by Einstein in 1905. He explained Brownian motion by assuming that the immersed particle was being subject to continuous bombardment by the molecules of the surrounding medium. A more concise and mathematical definition of Brownian motion was given by Wiener in a series of papers beginning in 1918. Wiener provided a concise definition of Brownian motion as a stochastic process.

Clearly, Brownian motion has its origins in science. However, it has proved extraordinarily useful in modeling the behavior of many economic variables, the most noteworthy being price. Indeed, just as the motion exhibited by small particles immersed in gas or liquid, prices in the stock market appear to fluctuate rather randomly leading some to believe that Brownian motion may be a good model for stock price behavior.

The purpose of this paper will be to discuss first in more detail the theory and mathematics underlying Brownian motion and then to test the empirical validity of Brownian motion as a model for stock behavior.

Department 1 Awarding Honors Status

Mathematics

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