 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-211/4/b/solution

{H_{T} \neq = 0, X_{T - 1} \leq 0}

H_{T} \cdot (M_{T} - M_{T - 1}) = X_{T} - X_{T - 1} \geq - X_{T - 1} \geq 0.

Dividing by

∥ H_{T} ∥

proves

ξ \geq 0

there; outside that event

ξ = 0

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