W_tis a Brownian motion under the actual measure andW_tis a Brownian motion under the equivalent risk-neutral measure.

With risk-free rate of interest r,

1. evaluate E^Q[S_T] where S_Tis the stock price at time T.

2. derive the Black-Scholes equation for an European Call Option C(t,S_t) from the dynamics of the stock price S_t,

dS_t= S_tdt + S_tdW_tand a portfolio = S_t C(t, S_t) where is the number of shares of the stock.