英文标题：
《How local in time is the no-arbitrage property under capital gains taxes
?》
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作者：
Christoph K\\\"uhn
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最新提交年份：
2018
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英文摘要：
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.
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中文摘要：
在无摩擦的金融市场中，无套利及时成为当地的财产。这意味着离散时间模型是无套利的当且仅当不存在单期套利时。对于资本利得税，这种等价性是失败的。对于一个具有线性税收和一只不可卖空风险股票的模型，我们引入了鲁棒局部无套利（RLNA）的概念，作为保证动态无套利的最弱局部条件。在一个尖锐的二分法条件下，我们证明了（RLNA）。由于无套利不需要单期套利，因此后者被夹在两个局部条件之间，这使得我们可以估计其非局部性。此外，我们构造了一个股票价格过程，使得同一股票中的两个多头头寸相互对冲。这种在无套利无摩擦市场（或具有比例交易成本的市场）中无法出现的令人困惑的现象被用来表明，如果概率空间是无限的，仅套利并不意味着存在等价的分离度量。最后，通过引入几个虚拟证券，我们证明了对资本收益征收线性税的模型可以写成具有比例交易成本的模型。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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