Suppose that a stock price S follows geometric Brownian motion with expected return μand volatil

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First, let's define the variable $X = ln(S)$. We can rewrite the stochastic differential equatio

Suppose that a stock price $S$ follows geometric Brownian motion with expected return $\mu$ and volatility $\sigma$ : $$ d S=\mu S d t+\sigma S d z $$ What is the process followed by the variable $S^n$ ? Show that $S^n$ also follows geometric Brownian motion.