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.

我们为拓扑向量格中的无套利概念提供了一个通用框架，其中涵盖了许多众所周知的无套利概念作为特殊情况。我们强加的主要结构条件是初始财富为零和初始财富为正的交易策略的结果具有凸锥结构。作为我们方法的一个结果，概念 NUPBR、NAA \(_1\)和 NA \(_1\)在我们的一般环境中可能无法等效。此外，我们推导出了资产定价基本定理 (FTAP) 的抽象版本，包括 Banach 函数空间上的抽象 FTAP，并研究了 FTAP 在其经典形式中何时需要分离度量。我们还考虑了一个不需要 numéraire 的具有半鞅的金融市场，并通过仅使用拓扑向量格的理论和众所周知的序列随机分析结果来推导出显示无套利概念之间联系的结果的简短证明。