 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-202/4/c/solution

s = [M]_{t}

s \to \infty

, and part b gives

M_{t} - \frac{1}{2} [M]_{t} = W_{s} - \frac{s}{2} = s (\frac{W _{s}}{s} - \frac{1}{2}) .

Since

W_{s} / s \to 0

almost surely, the expression tends to

- \infty

 New to topics? Read the docs here!