We show that the absence of arbitrage in a model with both fixed and proportional transaction costs is equivalent to the existence of a family of absolutely continuous single-step probability measures, together with an adapted process with values within the bid-ask intervals that satisfies the martingale property with respect to each of the measures. This extends Harrison and Pliska’s classical Fundamental Theorem of Asset Pricing to the case of combined fixed and proportional transaction costs.

中文翻译：

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固定和成比例交易成本下资产定价的基本定理

我们证明，在固定成本和成比例交易成本的模型中，套利的缺失等同于存在一个绝对连续的单步概率测度系列，以及一个在满足竞价区间的值范围内的自适应过程。关于每项措施的ting财产。这将Harrison和Pliska的经典资产定价基本定理扩展到固定和成比例交易成本组合的情况。