论文标题
离散时间金融市场中的交易限制下的套利概念
Arbitrage concepts under trading restrictions in discrete-time financial markets
论文作者
论文摘要
在离散时间的环境中，我们在存在凸交易限制的情况下研究套利概念。我们表明，投资组合优化问题的解决性等同于缺乏第一类套利，这种条件比经典缺乏套利机会弱。我们将基于投资组合优化参数的资产定价基本定理的市场表征分析并得出基本定理的分析。通过特别考虑一个离散的时间设置，我们简化了依赖半明星理论的现有结果和证据，从而可以清楚地了解所涉及的基本经济概念。我们在借贷约束下具有套利机会的单期因素模型的背景下，体现了这些概念以及一些意外情况。
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.
