Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 39 / 6 / b / Solution

Put $h=S_0-\mu /R$. The initial capital of the one-period quadratic hedge isDefine the minimum-norm one-period pricing weightIt is square integrable, and $\mathbb{E}[(S_1-\mu ){\xi }_1]=c$, soThe weight depends only on the asset prices and their first two moments, not on the claim. It can be negative, so this identity alone does not supply an equivalent martingale measure or a positive state-price density.