Stochastic Calculus

b) Consider a non-dividend paying asset X. The source of uncertainty is captured by a standard Brownian motion {W = W(t), > 0) . The price of this asset satisfies the stochastic differential equation dx (t) Adt + BdW (t), X (t) where A and B are constants. Let f(t, X) = In X (t). Using Ito's formula, show that df (t, X(t) ) = (A B 2 dt + BdW(t)