  In this article we propose a study of market models starting from a set of
axioms, as one does in the case of risk measures. We define a market model
simply as a mapping from the set of adapted strategies to the set of random
variables describing the outcome of trading. We do not make any concavity
assumptions. The first result is that under sequential upper-semicontinuity the
market model can be represented as a normal integrand. We then extend the
concept of no-arbitrage to this setup and study its consequences as the
super-hedging theorem and utility maximization. Finally, we show how to extend
the concepts and results to the case of vector-valued market models, an example
of which is the Kabanov model of currency markets.
