  We study contingent claims in a discrete-time market model where trading
costs are given by convex functions and portfolios are constrained by convex
sets. In addition to classical frictionless markets and markets with
transaction costs or bid-ask spreads, our framework covers markets with
nonlinear illiquidity effects for large instantaneous trades. We derive dual
characterizations of superhedging conditions for contingent claim processes in
a market without a cash account. The characterizations are given in terms of
stochastic discount factors that correspond to martingale densities in a market
with a cash account. The dual representations are valid under a topological
condition and a weak consistency condition reminiscent of the ``law of one
price'', both of which are implied by the no arbitrage condition in the case of
classical perfectly liquid market models. We give alternative sufficient
conditions that apply to market models with nonlinear cost functions and
portfolio constraints.
