The Development and Status of Brownian Motion in Finance Market

MA Jinlong^1,2, MA Feite² 

(1. Changsha Workroom of Nonlinear Special Dynamics, Changsha 410013, China,

2. Guangzhou Institute of Geochemistry Chinese Academy of Science, Guangzhou 510640, China)

Abstract: This paper discusses that the integrity system of financial economics (mathematical finance) is constructed by Brownian motion theory, and that the turning point is created by fractional Brownian motion for opening out the rule of financial market price-wave on the theory of complex systems. The way is demonstrated for speculating finance market’s trade price fluctuation by finity scale Brownian motion on the theory of complex systems, which is developing finance economics to a new field fractal dimension mathematical finance.

Key words: finance market; Brownian motion; fractal; fractional Brownian motion; finity scale Brownian motion