英文标题：
《A unified Framework for Robust Modelling of Financial Markets in
discrete time》
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作者：
Jan Obloj, Johannes Wiesel
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最新提交年份：
2019
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英文摘要：
We unify and establish equivalence between the pathwise and the quasi-sure approaches to robust modelling of financial markets in discrete time. In particular, we prove a Fundamental Theorem of Asset Pricing and a Superhedging Theorem, which encompass the formulations of [Bouchard, B., & Nutz, M. (2015). Arbitrage and duality in nondominated discrete-time models. The Annals of Applied Probability, 25(2), 823-859] and [Burzoni, M., Frittelli, M., Hou, Z., Maggis, M., & Obloj, J. (2019). Pointwise arbitrage pricing theory in discrete time. Mathematics of Operations Research]. In bringing the two streams of literature together, we also examine and relate their many different notions of arbitrage. We also clarify the relation between robust and classical $\\mathbb{P}$-specific results. Furthermore, we prove when a superhedging property w.r.t. the set of martingale measures supported on a set of paths $\\Omega$ may be extended to a pathwise superhedging on $\\Omega$ without changing the superhedging price.
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中文摘要：
我们统一并建立了离散时间金融市场稳健建模的路径方法和准确定方法之间的等价性。特别地，我们证明了资产定价的一个基本定理和一个超边缘定理，其中包括[Bouchard，B.，&Nutz，M.（2015）。非支配离散时间模型中的套利和对偶。应用概率年鉴，25（2），823-859]和[Burzoni，M.，Frittelli，M.，Hou，Z.，Maggis，M.，&Obloj，J.（2019）。离散时间点式套利定价理论。运筹学数学]。在将这两组文献汇集在一起的过程中，我们还研究并联系了他们对套利的许多不同概念。我们还阐明了鲁棒性和经典$\\ mathbb{P}$-特定结果之间的关系。此外，我们证明了在不改变超边缘价格的情况下，当一个超边缘性质w.r.t.在一组路径$\\ Omega$上支持的鞅测度集可以扩展为$\\ Omega$上的路径超边缘时。
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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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