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

Take expected values in the sharp power-call inequality. If $M(1+\epsilon )$ is finite, then for every $K\ge 0$,The bound is independent of the strike, soCombined 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.