 Solution

ID: past-exam-of-the-martingales-and-financial-mathematics-course-of-the-university-of-oxford/2010/a/2/b/i/solution

For any

λ > 0

, the variable

Z = ∣ X_{1} ∣/ λ

has infinite expectation. Part (a)(ii) therefore forces

\sum_{n} P (∣ X_{1} ∣ \geq λn) = \infty

. Identical distributions give

n \sum P (∣ X_{n} ∣ \geq λn) = \infty.

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