发帖
雷达卡
英文标题：
《A fundamental theorem of asset pricing for continuous time large
financial markets in a two filtration setting》
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作者：
Christa Cuchiero, Irene Klein and Josef Teichmann
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最新提交年份：
2017
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英文摘要：
We present a version of the fundamental theorem of asset pricing (FTAP) for continuous time large financial markets with two filtrations in an $L^p$-setting for $ 1 \\leq p < \\infty$. This extends the results of Yuri Kabanov and Christophe Stricker \\cite{KS:06} to continuous time and to a large financial market setting, however, still preserving the simplicity of the discrete time setting. On the other hand it generalizes Stricker\'s $L^p$-version of FTAP \\cite{S:90} towards a setting with two filtrations. We do neither assume that price processes are semi-martigales, (and it does not follow due to trading with respect to the \\emph{smaller} filtration) nor that price processes have any path properties, neither any other particular property of the two filtrations in question, nor admissibility of portfolio wealth processes, but we rather go for a completely general (and realistic) result, where trading strategies are just predictable with respect to a smaller filtration than the one generated by the price processes. Applications range from modeling trading with delayed information, trading on different time grids, dealing with inaccurate price information, and randomization approaches to uncertainty.
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中文摘要：
我们提出了连续时间大型金融市场的资产定价基本定理（FTAP）的一个版本，该市场在1美元/平方米/平方米/平方米的情况下有两个过滤。这将尤里·卡巴诺夫（YuriKabanov）和克里斯托夫·斯特里克（ChristopheStricker）的结果扩展到连续时间和大型金融市场环境，但仍然保持了离散时间环境的简单性。另一方面，它将Stricker的FTAP{s:90}的$L^p$版本推广到具有两个过滤的设置。我们既不假设价格过程是半马尔蒂加莱过程（由于交易涉及到较小的过滤），也不假设价格过程具有任何路径属性，既不具有所讨论的两个过滤的任何其他特定属性，也不具有投资组合财富过程的可采性，但我们更倾向于获得一个完全一般（和现实）的结果，在这种情况下，交易策略的可预测性仅限于比价格过程产生的过滤更小的过滤。应用范围包括用延迟信息建模交易、在不同时间网格上交易、处理不准确的价格信息以及随机方法处理不确定性。
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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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