Before revision:  We show that, in the typical scenario, the martingale measure is not unique , that there are non-replicable claims , and that the martingale prices can vary significantly; for instance, for a European put option, any positive real number is a martingale price for some martingale measure. In addition, the second moment of the hedging error for a strategy calculated via a given martingale measure can take any arbitrary positive value under some equivalent measure.
After revision:  We show that, in the typical scenario, the martingale measure is not unique , that there are non-replicable claims . It is shown that arbitrarily small deviations cause significant changes in the market properties. In particular, the martingale prices and the second moment of the hedging error for a strategy calculated via a given martingale measure can take any arbitrary positive value under some equivalent measure.