Dynamic trading under integer constraints
研究了在整数交易量约束下的离散时间交易，发现对于有理数价格影响不大，但对无理数价格则产生新的无套利定价和套期保值理论，并建立了相应的金融基本定理。
Abstract 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.