Arbitrage Theory under Integer Constraints

We investigate discrete time trading under integer constraints, that is, we assume that the offered goods or shares are traded in entire quantities instead of the usual real quantity assumption. For rational asset prices this... [ view full abstract ]

We investigate discrete time trading under integer constraints, that is, we assume that the offered goods or shares are traded in entire quantities instead of the usual real quantity assumption. For 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. Finally, we discuss superhedging with integral portfolios.