Mathematical Modeling in Finance with Stochastic Processes

(Ben Green) #1

5.2. THE DEFINITION OF BROWNIAN MOTION AND THE WIENER PROCESS 165


5.1 Graph of the Dow-Jones Industrial Average from August,


increments with the same mean and variance (brown line). to August 2009 (blue line) and a random walk with normal


the same mean and variance (brown line).


Figure 5.2: A standardized density histogram of daily close-to-close returns
on the Pepsi Bottling Group, symbol NYSE:PBG, from September 16, 2003
to September 15, 2003, up to September 13, 2006 to September 12, 2006

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