英文标题：
《Multiscale Asymptotic Analysis for Portfolio Optimization under
  Stochastic Environment》
---
作者：
Jean-Pierre Fouque, Ruimeng Hu
---
最新提交年份：
2019
---
英文摘要：
  Empirical studies indicate the presence of multi-scales in the volatility of underlying assets: a fast-scale on the order of days and a slow-scale on the order of months. In our previous works, we have studied the portfolio optimization problem in a Markovian setting under each single scale, the slow one in [Fouque and Hu, SIAM J. Control Optim., 55 (2017), 1990-2023], and the fast one in [Hu, Proceedings of IEEE CDC 2018, accepted]. This paper is dedicated to the analysis when the two scales coexist in a Markovian setting. We study the terminal wealth utility maximization problem when the volatility is driven by both fast- and slow-scale factors. We first propose a zeroth-order strategy, and rigorously establish the first order approximation of the associated problem value. This is done by analyzing the corresponding linear partial differential equation (PDE) via regular and singular perturbation techniques, as in the single-scale cases. Then, we show the asymptotic optimality of our proposed strategy within a specific family of admissible controls. Interestingly, we highlight that a pure PDE approach does not work in the multi-scale case and, instead, we use the so-called epsilon-martingale decomposition. This completes the analysis of portfolio optimization in both fast mean-reverting and slowly-varying Markovian stochastic environments.
---
中文摘要：
实证研究表明，标的资产波动存在多个尺度：以天为单位的快速尺度和以月为单位的缓慢尺度。在我们之前的工作中，我们研究了每个单尺度下马尔可夫环境下的投资组合优化问题，【Fouke and Hu，SIAM J.Control Optim.，55（2017），1990-2023】中的慢速投资组合优化问题，以及【Hu，IEEE CDC 2018年会议录，接受】中的快速投资组合优化问题。本文致力于分析两种尺度在马尔可夫背景下共存的情况。我们研究了当波动率同时由快尺度和慢尺度因素驱动时的终端财富效用最大化问题。我们首先提出了一种零阶策略，并严格地建立了相关问题值的一阶近似。这是通过分析相应的线性偏微分方程（PDE）通过正则和奇异摄动技术实现的，就像在单尺度情况下一样。然后，我们在一个特定的容许控制族中证明了我们提出的策略的渐近最优性。有趣的是，我们强调，纯偏微分方程方法在多尺度情况下不起作用，相反，我们使用所谓的ε鞅分解。这就完成了快速均值回复和缓慢变化马尔可夫随机环境下的投资组合优化分析。
---
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
--
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
--

---
PDF下载：
-->