We discuss the lognormal model of stock prices. We use the efficient market hypothesis as a justification for the Markov nature of the stochastic process. We use this to prove independent random increments of volatility. We use the fact that the expected return should not be a function of the total position size, but rather the relative position to construct our model. We use the Ito formula from Stochastic Calculus and use Brownian motion in our model.
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