 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-202/4/a/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

[M]_{T} \leq b

(M - M_{0}) /2

because

E exp (\frac{1}{8} [M]_{T}) \leq e^{b /8} < \infty.

Its stochastic exponential is therefore a true martingale with expectation one. Using the factorization from part (i),

E S_{T} \geq S_{0} e^{- b /8} E E (\frac{1}{2} (M - M_{0}))_{T} = S_{0} e^{- b /8} .

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