英文标题：
《Universal Arbitrage Aggregator in Discrete Time Markets under
Uncertainty》
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作者：
Matteo Burzoni, Marco Frittelli and Marco Maggis
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最新提交年份：
2015
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英文摘要：
In a model independent discrete time financial market, we discuss the richness of the family of martingale measures in relation to different notions of Arbitrage, generated by a class $\\mathcal{S}$ of significant sets, which we call Arbitrage de la classe $\\mathcal{S}$. The choice of $\\mathcal{S}$ reflects into the intrinsic properties of the class of polar sets of martingale measures. In particular: for S=${\\Omega}$ absence of Model Independent Arbitrage is equivalent to the existence of a martingale measure; for $\\mathcal{S}$ being the open sets, absence of Open Arbitrage is equivalent to the existence of full support martingale measures. These results are obtained by adopting a technical filtration enlargement and by constructing a universal aggregator of all arbitrage opportunities. We further introduce the notion of market feasibility and provide its characterization via arbitrage conditions. We conclude providing a dual representation of Open Arbitrage in terms of weakly open sets of probability measures, which highlights the robust nature of this concept.
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中文摘要：
在一个独立于模型的离散时间金融市场中，我们讨论了由一类$\\mathcal{S}$有效集生成的与不同套利概念有关的鞅测度族的丰富性，我们称之为套利de la classe$\\mathcal{S}$。$\\mathcal{S}$的选择反映了鞅测度的极集合类的内在性质。特别是：对于S=${\\Omega}$，没有模型独立的套利等价于鞅测度的存在；当$\\mathcal{S}$是开集时，没有开套利等价于存在完全支持鞅测度。这些结果是通过采用技术过滤放大和构建所有套利机会的通用聚合器获得的。我们进一步引入了市场可行性的概念，并通过套利条件对其进行了描述。最后，我们给出了开放套利的概率测度弱开放集的对偶表示，这突出了这个概念的鲁棒性。
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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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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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