英文标题：
《Asymptotic Optimal Portfolio in Fast Mean-reverting Stochastic
  Environments》
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作者：
Ruimeng Hu
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最新提交年份：
2019
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英文摘要：
  This paper studies the portfolio optimization problem when the investor\'s utility is general and the return and volatility of the risky asset are fast mean-reverting, which are important to capture the fast-time scale in the modeling of stock price volatility. Motivated by the heuristic derivation in [J.-P. Fouque, R. Sircar and T. Zariphopoulou, \\emph{Mathematical Finance}, 2016], we propose a zeroth order strategy, and show its asymptotic optimality within a specific (smaller) family of admissible strategies under proper assumptions. This optimality result is achieved by establishing a first order approximation of the problem value associated to this proposed strategy using singular perturbation method, and estimating the risk-tolerance functions. The results are natural extensions of our previous work on portfolio optimization in a slowly varying stochastic environment [J.-P. Fouque and R. Hu, \\emph{SIAM Journal on Control and Optimization}, 2017], and together they form a whole picture of analyzing portfolio optimization in both fast and slow environments.
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中文摘要：
本文研究了当投资者效用一般且风险资产的收益率和波动率均为快速均值回复时的投资组合优化问题，这对于获取股票价格波动建模中的快速时间尺度非常重要。受[J.-P.Fouke，R.Sircar和T.Zariphopoulou，\\emph{数学金融}，2016]中启发式推导的启发，我们提出了一个零阶策略，并在适当的假设下证明了其在特定（较小）容许策略族中的渐近最优性。通过使用奇异摄动法建立与该策略相关的问题值的一阶近似值，并估计风险容限函数，可获得该优化结果。这些结果是我们之前在缓慢变化的随机环境中的投资组合优化工作的自然延伸【J.-P.Fouque和R.Hu，emph{SIAM Journal on Control and optimization}，2017年】，它们共同构成了在快速和慢速环境中分析投资组合优化的全貌。
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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：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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