(a) (10 points) Apply Ito's lemma to calculate dXt whete Xt = e^?t+ ?(2)Bt and where Bt is a standard Brownian motion. Is e^?t+ ?(2)Bt a martingale? Explain.

(b) (10 points) Calculate the (unconditional) expectation E[(Bs + Bt)Bu], for s ? t ? u where Bt is a standard Brownian motion.

(c) (10 points) Apply Ito's lemma to calculate dX, for Xt = Belo Bsds where B, is a stan- dxt dard Brownian motion. Calculate the instantaneous expected rate of return 1Et Xt