 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-3/29k/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

θ = \frac{μ + \frac{1}{2} σ ^{2} - r}{σ}

Q

F_{T}

\frac{d Q}{d P} = exp (- θ W_{T} - \frac{1}{2} θ^{2} T) .

W_{t}^{Q} = W_{t} + θt

Q

. Therefore

S_{t} = S_{0} exp ((r - \frac{1}{2} σ^{2}) t + σ W_{t}^{Q}) .

The discounted stock is an exponential Brownian martingale, so

e^{- r t} S_{t}

is a

Q

Q

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