标题： 理想化金融市场中的粗糙路径 显示英文标题

标题： Rough paths in idealized financial markets

摘要： 本文考虑理想化市场中金融资产的价格路径。其主要结果是，典型价格路径的变分指数最多为2，在这个意义上，典型价格路径不会比布朗运动的典型路径更粗糙。我们没有做出任何随机假设，只假设价格路径是正的且右连续的。"典型"这一限定词意味着存在一种交易策略（在证明中明确构造），该策略仅承担一个货币单位的风险，但当实现的价格路径的变分指数超过2时，将带来无限资本。本文还回顾了一些关于连续价格路径的已知结果，并列出了几个开放性问题。 显示英文摘要

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.