In frictionless financial markets, no-arbitrage is a local property in time. This means that a discrete time model is arbitrage-free if and only if there does not exist a one-period-arbitrage. With capital gains taxes, this equivalence fails. For a model with a linear tax and one non-shortable risky stock, we introduce the concept of robust local no-arbitrage (RLNA) as the weakest local condition which guarantees dynamic no-arbitrage. Under a sharp dichotomy condition, we prove (RLNA). Since no-one-period-arbitrage is necessary for no-arbitrage, the latter is sandwiched between two local conditions, which allows us to estimate its non-locality. Furthermore, we construct a stock price process such that two long positions in the same stock hedge each other. This puzzling phenomenon that cannot occur in arbitrage-free frictionless markets (or markets with proportional transaction costs) is used to show that no-arbitrage alone does not imply the existence of an equivalent separating measure if the probability space is infinite. Finally, we show that the model with a linear tax on capital gains can be written as a model with proportional transaction costs by introducing several fictitious securities.

中文翻译：

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资本利得税下的无套利财产在时间上有多大？

在无摩擦的金融市场中，及时套利是当地的财产。这意味着，当且仅当不存在一个周期的套利时，离散时间模型才是无套利的。使用资本利得税时，这种等效性将失败。对于具有线性税和一只不可卖空风险股票的模型，我们引入了稳健的本地无套利概念（RLNA）是保证动态无套利的最弱本地条件。在尖锐的二分法条件下，我们证明（RLNA）。由于无周期套利对无套利是必要的，因此无套利被夹在两个局部条件之间，这使我们能够估计其非局部性。此外，我们构建了一个股票价格过程，以使同一只股票中的两个多头头寸彼此对冲。这种在无套利的无摩擦市场（或具有成比例交易成本的市场）中不会发生的令人费解的现象被用来表明，如果概率空间是无限的，仅无套利并不意味着存在等效的分离措施。最后，我们证明通过引入几种虚拟证券，可以将对资本收益征收线性税的模型写为具有成比例交易成本的模型。