摘要翻译：
本文考虑了在理想化市场中金融证券的可能价格路径。其主要结果是典型价格路径的变异指数至多为2，在这个意义上，典型价格路径并不比布朗运动的典型路径粗糙。我们不做任何随机假设，只假设价格路径是正的和右连续的。“典型”的限定是指存在一种交易策略（在证明中明确构造），当已实现的价格路径的变异指数超过2时，只冒一个货币单位的风险，却带来无限大的资本。本文还回顾了关于连续价格路径的一些已知结果，并列出了几个尚待解决的问题。
---
英文标题：
《Rough paths in idealized financial markets》
---
作者：
Vladimir Vovk
---
最新提交年份：
2016
---
分类信息：

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
--
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
--

---
英文摘要：
  This paper considers possible price paths of a financial security in an idealized market. Its main result is that the variation index of typical price paths is at most 2, in this sense, typical price paths are not rougher than typical paths of Brownian motion. We do not make any stochastic assumptions and only assume that the price path is positive and right-continuous. The qualification "typical" means that there is a trading strategy (constructed explicitly in the proof) that risks only one monetary unit but brings infinite capital when the variation index of the realized price path exceeds 2. The paper also reviews some known results for continuous price paths and lists several open problems.
---
PDF链接：
https://arxiv.org/pdf/1005.0279