英文标题：
《Prospective strict no-arbitrage and the fundamental theorem of asset
pricing under transaction costs》
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作者：
Christoph K\\\"uhn and Alexander Molitor
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最新提交年份：
2019
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英文摘要：
In discrete time markets with proportional transaction costs, Schachermayer (2004) shows that robust no-arbitrage is equivalent to the existence of a strictly consistent price system. In this paper, we introduce the concept of prospective strict no-arbitrage that is a variant of the strict no-arbitrage property from Kabanov, R\\\'asonyi, and Stricker (2002). The prospective strict no-arbitrage condition is slightly weaker than robust no-arbitrage, and it implies that the set of portfolios attainable from zero initial endowment is closed in probability. A weak version of prospective strict no-arbitrage turns out to be equivalent to the existence of a consistent price system. In contrast to the fundamental theorem of asset pricing of Schachermayer (2004), the consistent frictionless prices may lie on the boundary of the bid-ask spread. On the technical level, a crucial difference to Schachermayer (2004) and Kabanov-R\\\'asonyi-Stricker (2003) is that we prove closedness without having at hand that the null-strategies form a linear space.
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中文摘要：
在具有比例交易成本的离散时间市场中，Schachermayer（2004）证明了鲁棒无套利等价于存在严格一致的价格系统。在本文中，我们引入了前瞻性严格无套利的概念，这是Kabanov、R\\asonyi和Stricker（2002）的严格无套利性质的一个变体。预期严格无套利条件略弱于稳健无套利条件，这意味着从零初始禀赋获得的投资组合集在概率上是封闭的。预期严格无套利的弱版本被证明等同于一致价格体系的存在。与Schachermayer（2004）的资产定价基本定理相反，一致的无摩擦价格可能位于买卖价差的边界上。在技术层面上，与Schachermayer（2004）和Kabanov-R\\asonyi-Stricker（2003）的一个关键区别在于，我们证明了接近性，而没有现成的零策略形成线性空间。
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分类信息：

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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