an:06948969
Zbl 1416.91347
Gerhold, Stefan; Kr??hner, Paul
Dynamic trading under integer constraints
EN
Finance Stoch. 22, No. 4, 919-957 (2018).
00415778
2018
j
91G10 60G44
arbitrage; hedging; integer constraints
Summary: 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 not necessarily an interval, but is either empty or dense in an interval. We also discuss superhedging with integer-valued portfolios.