  We consider the pricing and hedging of exotic options in a model-independent
set-up using \emph{shortfall risk and quantiles}. We assume that the marginal
distributions at certain times are given. This is tantamount to calibrating the
model to call options with discrete set of maturities but a continuum of
strikes. In the case of pricing with shortfall risk, we prove that the minimum
initial amount is equal to the super-hedging price plus the inverse of the
utility at the given shortfall level. In the second result, we show that the
quantile hedging problem is equivalent to super-hedging problems for knockout
options. These results generalize the duality results of [5,6] to the model
independent setting of [1].
