Hi Tutors,

Can anyone answer these questions - this is your challenge as no one has been able to yet?

Question 2. Product rule. Recall Ito's formula in two dimensions (in class we had m dimensions), dg( Xt, Yt) = Org(Xt, Yi)dX+ + dug(Xt, Yi)dY + 5 3 19 ( Xu Y)(dx )? + dung ( X, Y)(dy) + 20ng (X, Y )dX,dy., where g(x, y) is a twice-differentiable function, where dXt = ux(t, X )dt + Ox (t, X.)dBx,: and dY = My (t, Yo )dt + oy(t, Y.)dBy, and where Bx. and By are each 1-dimensional Brownian motions with correlation p. (a) What is the SDE followed by X, Y? (b) In ordinary calculus, we have the integration-by-parts formula, f(t)g'(t)dt = f(T)g(T) - f(0)g(0) - f' (t)g(t) dt. o What is the analogous integration-by-parts formula in stochastic calculus, with f being played by X and g being played by Y? Hint: integrate the answer to the previous question and rearrange