 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ii/paper-2/29k/i/solution

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

Let

ϕ = (ϕ_{n}^{0}, ϕ_{n}^{1}, \dots, ϕ_{n}^{d})

be a predictable self-financing portfolio, and let

V_{n}^{ϕ} = ϕ_{n} \cdot S_{n}

be its value. An arbitrage is such a strategy with

V_{0}^{ϕ} = 0, V_{T}^{ϕ} \geq 0 almost surely, P (V_{T}^{ϕ} > 0) > 0.

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