How to prove question 4a
4. (5 marks) Ito calculus. (a) Let X(t) and Y(t) be two stochastic processes, such that dx = ux(X(t), t )dt + ox (X(t), t ) dZx dY = my (Y (t), t )dt + oy (Y (t), t)dZy with Zx(t), Zy(t) being Brownian motions. Let X(t;) = X; and Y(t;) = Y;. Show that (Xit1 - Xi)(Yitl - Yi) = XitIYitl - XiYi - Xi( Yit1 - Yi) - Yi(Xit1 - Xi) . Now, using the definition of the Ito integral which is the limit of a discrete sum, show that X (s)dy (s) = [XY]b - Y(s)dX(s) - /dX(s)dY(s).
This question was created from hw1.pdf
321,403 students got unstuck by Course
Hero in the last week
Our Expert Tutors provide step by step solutions to help you excel in your courses