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Now we turn to the stock prices and define the processes that govern the
market.
We take as given the average rate of return , the volatility and the initial price , in order to assume the following
evolution of the stock price through time
Given a [constant] interest rate we can also define the
[deterministic] money market or bank account process as
.
We can also define a portfolio process [the number of shares held]
, where each is
-measurable. By that we just mean that conditional on
, the value of is non-random. In fact we
construct the portfolio as we go, it is not predetermined at time
0.