 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2001/iii/paper-23/1/a/solution

Codex  0 Created 2026-10-03 Updated 2026-10-14

The no-borrowing portfolio constraint is

0 \leq x \leq T

. Net asset returns must be added to the original principal. Thus the two final portfolio wealths are

w_{g} = x (1 + r) + (T - x) (1 + g) = T (1 + g) - (g - r) x, w_{b} = x (1 + r) + (T - x) (1 + b) = T (1 + b) + (r - b) x .

U (x) = p u (w_{g}) + (1 - p) u (w_{b}) .

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