英文标题：
《Pathwise stochastic integrals for model free finance》
---
作者：
Nicolas Perkowski, David J. Pr\\\"omel
---
最新提交年份：
2016
---
英文摘要：
We present two different approaches to stochastic integration in frictionless model free financial mathematics. The first one is in the spirit of It\\^o\'s integral and based on a certain topology which is induced by the outer measure corresponding to the minimal superhedging price. The second one is based on the controlled rough path integral. We prove that every \"typical price path\" has a naturally associated It\\^o rough path, and justify the application of the controlled rough path integral in finance by showing that it is the limit of non-anticipating Riemann sums, a new result in itself. Compared to the first approach, rough paths have the disadvantage of severely restricting the space of integrands, but the advantage of being a Banach space theory. Both approaches are based entirely on financial arguments and do not require any probabilistic structure.
---
中文摘要：
在无摩擦模型的金融数学中，我们提出了两种不同的随机积分方法。第一种是基于它的积分精神，基于一种特定的拓扑结构，这种拓扑结构由对应于最小超边缘价格的外部测度所诱导。第二种是基于受控粗糙路径积分的。我们证明了每一条“典型价格路径”都有一条自然关联的粗糙路径，并证明了受控粗糙路径积分是非预期黎曼和的极限，这本身就是一个新的结果，从而证明了它在金融学中的应用。与第一种方法相比，粗糙路径的缺点是严重限制了被积函数的空间，但其优点是作为一种Banach空间理论。这两种方法都完全基于财务论证，不需要任何概率结构。
---
分类信息：

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
--
一级分类：Quantitative Finance 数量金融学
二级分类：General Finance 一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
--

---
PDF下载：
-->