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ERIC Number: EJ939749
Record Type: Journal
Publication Date: 2004
Pages: 19
Abstractor: As Provided
Reference Count: 14
ISSN: ISSN-1051-1970
A Simplified Treatment of Brownian Motion and Stochastic Differential Equations Arising in Financial Mathematics
Parlar, Mahmut
PRIMUS, v14 n3 p269-287 2004
Brownian motion is an important stochastic process used in modelling the random evolution of stock prices. In their 1973 seminal paper--which led to the awarding of the 1997 Nobel prize in Economic Sciences--Fischer Black and Myron Scholes assumed that the random stock price process is described (i.e., generated) by Brownian motion. Despite its relative simplicity, the description of Brownian motion in advanced textbooks sometimes lacks an intuitive basis. The present exposition attempts to provide a simplified construction of standard Brownian motion based on a gambling analogy. This is followed by a description and explicit solution of two stochastic differential equations (known as arithmetic and geometric Brownian motion processes) that are driven by the standard Brownian motion process. The paper also illustrates the use of the Maple computer algebra system to simulate the standard and geometric Brownian motion processes. (Contains 2 figures.)
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A