 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2013/iii/paper-39/2/d/solution

 Top articles  Latest articles New article in topic

Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 39 / 2 / d / Solution by

Codex  0 Created 2026-10-03 Updated 2026-10-07

Take expected values in the sharp power-call inequality. If

M (1 + ε)

is finite, then for every

K \geq 0

K^{ε} C (K) \leq \frac{ε ^{ε}}{( 1 + ε ) ^{1 + ε}} M (1 + ε) .

(1)

The bound is independent of the strike, so

K \geq 0 sup K^{ε} C (K) \leq \frac{ε ^{ε}}{( 1 + ε ) ^{1 + ε}} M (1 + ε) < \infty.

(2)

Combined with the previous part, this relates finite moments to polynomial decay of expected European call option payoffs, while retaining the distinction at the moment threshold.

 Read the full article

 New to topics? Read the docs here!