LetW(t) be a standard Brownian motion andX(t) =e^W(t).

a)Show thatX(t) is not a martingale.

b)Show thate^(t/2X(t)) is a martingale.

c) Show that for any constant cR, the processY(t)=e^(cW(t)1/2c^2t)is a martingale.

d) Show thatE{e^(W(s)+W(t))}=e^(s+t/2)e^min{s,t}