英文标题：
《Optimal Portfolio under Fast Mean-reverting Fractional Stochastic
Environment》
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作者：
Jean-Pierre Fouque, Ruimeng Hu
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最新提交年份：
2018
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英文摘要：
Empirical studies indicate the existence of long range dependence in the volatility of the underlying asset. This feature can be captured by modeling its return and volatility using functions of a stationary fractional Ornstein--Uhlenbeck (fOU) process with Hurst index $H \\in (\\frac{1}{2}, 1)$. In this paper, we analyze the nonlinear optimal portfolio allocation problem under this model and in the regime where the fOU process is fast mean-reverting. We first consider the case of power utility, and rigorously give first order approximations of the value and the optimal strategy by a martingale distortion transformation. We also establish the asymptotic optimality in all admissible controls of a zeroth order trading strategy. Then, we extend the discussions to general utility functions using the epsilon-martingale decomposition technique, and we obtain similar asymptotic optimality results within a specific family of admissible strategies.
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中文摘要：
实证研究表明，标的资产的波动性存在长期依赖性。这一特征可以通过使用平稳的分数奥恩斯坦-乌伦贝克（fOU）过程的函数来建模其收益率和波动率，赫斯特指数为$H（\\frac{1}{2}，1）$。在本文中，我们分析了该模型下以及在fOU过程是快速均值回复的情况下的非线性最优投资组合分配问题。我们首先考虑了电力效用的情况，并通过鞅失真变换严格地给出了一阶近似值和最优策略。我们还建立了零阶交易策略所有容许控制的渐近最优性。然后，我们利用epsilon鞅分解技术将讨论扩展到一般效用函数，并在特定的容许策略族中获得类似的渐近最优性结果。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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