英文标题：
《Portfolio Optimization under Fast Mean-reverting and Rough Fractional
  Stochastic Environment》
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作者：
Jean-Pierre Fouque, Ruimeng Hu
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最新提交年份：
2019
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英文摘要：
  Fractional stochastic volatility models have been widely used to capture the non-Markovian structure revealed from financial time series of realized volatility. On the other hand, empirical studies have identified scales in stock price volatility: both fast-time scale on the order of days and slow-scale on the order of months. So, it is natural to study the portfolio optimization problem under the effects of dependence behavior which we will model by fractional Brownian motions with Hurst index $H$, and in the fast or slow regimes characterized by small parameters $\\eps$ or $\\delta$. For the slowly varying volatility with $H \\in (0,1)$, it was shown that the first order correction to the problem value contains two terms of order $\\delta^H$, one random component and one deterministic function of state processes, while for the fast varying case with $H > \\half$, the same form holds at order $\\eps^{1-H}$. This paper is dedicated to the remaining case of a fast-varying rough environment ($H < \\half$) which exhibits a different behavior. We show that, in the expansion, only one deterministic term of order $\\sqrt{\\eps}$ appears in the first order correction.
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中文摘要：
分数阶随机波动率模型被广泛用于捕捉已实现波动率的金融时间序列所揭示的非马尔可夫结构。另一方面，实证研究确定了股票价格波动的尺度：以天为单位的快速时间尺度和以月为单位的缓慢时间尺度。因此，研究依赖行为影响下的投资组合优化问题是很自然的，我们将用赫斯特指数为$H$的分数布朗运动来建模，并以小参数为$eps$或$delta$的快速或慢速区域为特征。对于在（0,1）$中缓慢变化的波动率，对问题值的一阶修正包含两项$\\delta^H$、一个随机分量和一个状态过程的确定函数，而对于快速变化的情况，在$\\eps ^{1-H}$中，相同的形式保持在$\\eps ^{1-H}$。本文致力于研究快速变化的粗糙环境（H<0.5美元）表现出不同行为的剩余情况。我们证明，在展开式中，在一阶修正中只出现一个$\\ sqrt{\\ eps}$阶的确定性项。
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分类信息：

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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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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