 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ib/paper-1/18h/b/solution

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

The probability of no recovery through month

M

is the product of the conditional survival probabilities, so

γ = 1 - t = 1 \prod M (1 - q_{t}) .

E [1 - q_{t} ∣ X] = \frac{1 + r _{t} - d _{t}}{T + 1 + r _{t}} .

Consequently

γ_{B} = 1 - t = 1 \prod M \frac{1 + r _{t} - d _{t}}{T + 1 + r _{t}} .

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