The seller of a contingent claim H can always find a self-financing investment strategy that (super)hedges the claim H. When the seller wants to endow an initial capital x less than the one required to get perfect (super)hedging, the shortfall risk minimisation problem arises in a natural way. The aim is to find the strategy that minimises E{`([H(ST )−V x,φ T ])} (shortfall risk), where V x,φ t...