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Assume an asset price S_{t} follows the geometric Brownian motion, dS_{t} = µS_{t}d_{t} + σS_{t}dW_{t}, 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 X_{t} = S_{t}^{n} , where n is a constant.
2. Compute E[X_{t}] and Var[X_{t}].
3. Using the Ito's Lemma find the stochastic differential equation satisfied by the process Y_{t} = S_{t}e^{rt} .
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