This paper presents a stochastic model for discrete-time trading in financial
markets where trading costs are given by convex cost functions and portfolios
are constrained by convex sets. The model does not assume the existence of a
cash account (a perfectly liquid asset that can be traded without
restrictions). 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. In the presence
of nonlinearities, the classical notion of free lunch turns out to have two
equally meaningful generalizations, a marginal and a scalable one. Using
techniques of convex analysis we give martingale characterizations of both in
the spirit of the fundamental theorem of asset pricing.