Fix a filtered probability space (S, F, (Ft), P) supporting a one-dimensional standard Brown- ian motion W. Let T > 0 be a fixed time horizon. Suppose that the process Y satisfies the stochastic differential equation dyt = b(t, Yt) dt + o(t, Yt) dWt, (5) for some functions (t, y) > b(t, y) and (t, y) - o(t, y). Given a constant y * 0, determine a PDE and appropriate boundary conditions that a C'1,2 function (t, y) > f(t, y) should satisfy to admit the expression f ( t, Y t ) = e 27t+WtEP ez72 T -YWTF(Yr) |Ft , fortST. (6) If required, you may assume that all random variables are integrable and that all stochastic integrals with respect to a standard Brownian motion are martingales