  In this paper we investigate discrete time trading under integer constraints,
that is, we assume that the offered goods or shares are traded in integer
quantities instead of the usual real quantity assumption. For finite
probability spaces and rational asset prices this has little effect on the core
of the theory of no-arbitrage pricing. For price processes not restricted to
the rational numbers, a novel theory of integer arbitrage free pricing and
hedging emerges. We establish an FTAP, involving a set of absolutely continuous
martingale measures satisfying an additional property. The set of prices of a
contingent claim is no longer an interval, but is either empty or dense in an
interval. We also discuss superhedging with integral portfolios.
