In a discrete-time setting, we study arbitrage concepts in the presence of convex trading constraints. We show that solvability of portfolio optimization problems is equivalent to absence of arbitrage of the first kind, a condition weaker than classical absence of arbitrage opportunities. We center our analysis on this characterization of market viability and derive versions of the fundamental theorems of asset pricing based on portfolio optimization arguments. By considering specifically a discrete-time setup, we simplify existing results and proofs that rely on semimartingale theory, thus allowing for a clear understanding of the foundational economic concepts involved. We exemplify these concepts, as well as some unexpected situations, in the context of one-period factor models with arbitrage opportunities under borrowing constraints.

中文翻译：

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离散时间金融市场交易限制下的套利概念

在离散时间设置中，我们研究存在凸交易约束的套利概念。我们表明，投资组合优化问题的可解性相当于没有第一类套利，这种情况比经典的没有套利机会要弱。我们将分析集中在市场可行性的这种特征上，并根据投资组合优化参数推导出资产定价基本定理的版本。通过专门考虑离散时间设置，我们简化了依赖于半鞅理论的现有结果和证明，从而可以清楚地理解所涉及的基本经济概念。我们在借款约束下具有套利机会的单期因子模型的背景下，举例说明了这些概念以及一些意外情况。