Exercise 5.4. Let Bt be a standard Brownian motion with Bo = 0. Let m > 0 and let X = emB 1. Find a function g such that Mt := Xt exp >{ g(Xs) ds } is a local martingale. 2. What SDE does Mt satisfy? 3. Let Q be the probability measure obtained by tilting by Mt. Find the SDE for Bt in terms of a Q-Brownian motion. 4. Explain why Mt is actually a martingale.