 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-3/29l/a/solution

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

Let

V (n, x)

be maximal expected utility from dates

n + 1, \dots, N

plus terminal wealth, given

X_{n} = x

. Then

V (N, x) = U (x)

and

V (n, x) = c, h sup {U (c) + E [V (n + 1, x - c + h R_{n + 1})]} .

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