英文标题：
《Fractional Brownian motion with zero Hurst parameter: a rough volatility
viewpoint》
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作者：
Eyal Neuman and Mathieu Rosenbaum
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最新提交年份：
2018
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英文摘要：
Rough volatility models are becoming increasingly popular in quantitative finance. In this framework, one considers that the behavior of the log-volatility process of a financial asset is close to that of a fractional Brownian motion with Hurst parameter around 0.1. Motivated by this, we wish to define a natural and relevant limit for the fractional Brownian motion when $H$ goes to zero. We show that once properly normalized, the fractional Brownian motion converges to a Gaussian random distribution which is very close to a log-correlated random field.
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中文摘要：
粗糙波动率模型在定量金融中越来越流行。在这个框架中，我们认为金融资产的对数波动过程的行为接近于分数布朗运动，赫斯特参数约为0.1。基于此，我们希望在$H$为零时，定义分数布朗运动的一个自然的和相关的极限。我们证明，一旦适当归一化，分数布朗运动收敛到高斯随机分布，该分布非常接近对数相关随机常
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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
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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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