Rough paths in idealized financial markets
Rough paths in idealized financial markets
复制标题
理想化金融市场的崎岖道路
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
V. Vovk
中科院分区：
文献类型：
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作者：
V. Vovk
本文考虑了理想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，只假设价格路径是右连续的。限定词“典型”意味着存在一种交易策略（在证明中明确构建），该交易策略仅承担一个货币单位的风险，但当已实现价格路径的变化指数超过2时，会带来无限的资本。本文还回顾了连续价格路径的一些已知结果。
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 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.