We study the Fundamental Theorem of Asset Pricing for a general financial market under Knightian Uncertainty. We adopt a functional analytic approach which requires neither specific assumptions on the class of priors \(\mathcal {P}\) nor on the structure of the state space. Several aspects of modeling under Knightian Uncertainty are considered and analyzed. We show the need for a suitable adaptation of the notion of No Free Lunch with Vanishing Risk and discuss its relation to the choice of an appropriate technical filtration. In an abstract setup, we show that absence of arbitrage is equivalent to the existence of approximate martingale measures sharing the same polar set of \(\mathcal {P}\). We then specialize our results to a discrete-time financial market in order to obtain martingale measures.

中文翻译：

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骑士不确定性下的无套利建模

我们研究了基于Knightian不确定性的一般金融市场的资产定价基本定理。我们采用功能分析方法，该方法既不需要对先验类\（\ mathcal {P} \）进行特定假设，也不需要状态空间的结构。考虑并分析了Knightian不确定性下建模的几个方面。我们表明有必要对“零风险无免费午餐”的概念进行适当调整，并讨论其与选择适当技术过滤的关系。在一个抽象的设置中，我们表明没有套利等同于存在共享相同极性集\（\ mathcal {P} \）的近似mar度量。然后，我们将结果专门用于离散时间的金融市场，以便获得mar测度。