拓扑向量格中的无套利概念
No-arbitrage concepts in topological vector lattices
AI总结：
本文在拓扑向量格框架下提出无套利概念的通用理论，推导了资产定价基本定理的抽象版本，并探讨了无套利概念之间的联系。
摘要：
我们为拓扑向量格中的无套利概念提供了一个通用框架，该框架涵盖了许多已知的无套利概念作为特例。我们主要的结构性条件是，初始财富为零和正初始财富的交易策略的结果具有凸锥的结构。作为我们方法的一个结果，概念NUPBR、NAA₁和NA₁在我们的通用设定中可能不等价。此外，我们推导了资产定价基本定理（FTAP）的抽象版本，包括在Banach函数空间上的抽象FTAP，并研究了在经典形式下FTAP何时有保障。我们还考虑了一个不需要数钱的半鞅金融市场，并推导了结果，这些结果仅使用拓扑向量格的理论和已知的随机分析结果，在一系列简短的证明中建立了无套利概念之间的联系。
英文摘要：
We provide a general framework for no-arbitrage concepts in topological vector lattices, which covers many of the well-known no-arbitrage concepts as particular cases. The main structural condition we impose is that the outcomes of trading strategies with initial wealth zero and those with positive initial wealth have the structure of a convex cone. As one consequence of our approach, the concepts NUPBR, NAA$_1$ and NA$_1$ may fail to be equivalent in our general setting. Furthermore, we derive abstract versions of the fundamental theorem of asset pricing (FTAP), including an abstract FTAP on Banach function spaces, and investigate when the FTAP is warranted in its classical form with a separating measure. We also consider a financial market with semimartingales which does not need to have a numéraire, and derive results which show the links between the no-arbitrage concepts by only using the theory of topological vector lattices and well-known results from stochastic analysis in a sequence of short proofs.
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