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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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