### Assume an asset price follows the geometric brownian motion

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Assume an asset price St follows the geometric Brownian motion, dSt = µStdt + σStdWt, where µ and σ are constants and r is the risk-free rate.

1. Using the Ito's Lemma find the stochastic differential equation satisfied by the process Xt = Stn , where n is a constant.

2. Compute E[Xt] and Var[Xt].

3. Using the Ito's Lemma find the stochastic differential equation satisfied by the process Yt = Stert .

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