In discrete-time markets with proportional transaction costs, Schachermayer (Math. Financ. 14:19–48, 2004) showed that robust no-arbitrage is equivalent to the existence of a strictly consistent price system. In this paper, we introduce the concept of prospective strict no-arbitrage that is a variant of the strict no-arbitrage property from Kabanov et al. (Finance Stoch. 6:371–382, 2002). The prospective strict no-arbitrage condition is slightly weaker than the robust no-arbitrage condition, and it implies that the set of portfolios attainable from zero initial endowment is closed in probability. A weak version of prospective strict no-arbitrage turns out to be equivalent to the existence of a consistent price system. In contrast to the fundamental theorem of asset pricing of Schachermayer (Math. Financ. 14:19–48, 2004), the consistent frictionless prices may lie on the boundary of the bid–ask spread. On the technical level, a crucial difference to Schachermayer (Math. Financ. 14:19–48, 2004) and Kabanov et al. (Finance Stoch. 7:403–411, 2003) is that we prove closedness without having at hand that the null-strategies form a linear space.

中文翻译：

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准严格无套利和交易成本下资产定价的基本定理

在具有成比例交易成本的离散时间市场中，Schachermayer（Math。Financ。14：19-48，2004）表明，稳健的无套利行为等同于存在严格一致的价格体系。在本文中，我们引入的概念预期严格的无套利这是一个变种严格的无套利Kabanov等人的财产。（Finance Stoch。6：371–382，2002）。预期的严格无套利条件比健壮的无套利条件稍弱，这意味着从零初始end赋中可获得的投资组合的概率是封闭的。预期的严格无套利的弱势形式等同于存在一致的价格体系。与Schachermayer资产定价的基本定理（Math。Financ。14：19-48，2004）相反，一致的无摩擦价格可能位于买卖价差的边界。在技​​术层面上，与Schachermayer（Math。Financ。14：19-48，2004）和Kabanov等人的论文有重大区别。（Finance Stoch。7：403-411，2003）是，我们证明了封闭性，而无需立即掌握零策略形成一个线性空间。