  In an incomplete market the price of a claim f in general cannot be uniquely
identified by no arbitrage arguments. However, the ``classical'' super
replication price is a sensible indicator of the (maximum selling) value of the
claim. When f satisfies certain pointwise conditions (e.g., f is bounded from
below), the super replication price is equal to sup_QE_Q[f], where Q varies on
the whole set of pricing measures. Unfortunately, this price is often too high:
a typical situation is here discussed in the examples. We thus define the less
expensive weak super replication price and we relax the requirements on f by
asking just for ``enough'' integrability conditions. By building up a proper
duality theory, we show its economic meaning and its relation with the
investor's preferences. Indeed, it turns out that the weak super replication
price of f coincides with sup_{Q\in M_{\Phi}}E_Q[f], where M_{\Phi} is the
class of pricing measures with finite generalized entropy (i.e., E[\Phi
(\frac{dQ}{dP})]<\infty) and where \Phi is the convex conjugate of the utility
function of the investor.
