Assume an asset price stnbspfollows the geometric brownian

Question

Assume an asset price S_t follows the geometric Brownian motion, dS_t = µS_td_t + σS_tdW_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_tⁿ , 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_te^rt .