英文标题：
《Optimal Portfolio under Fractional Stochastic Environment》
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作者：
Jean-Pierre Fouque, Ruimeng Hu
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最新提交年份：
2017
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英文摘要：
Rough stochastic volatility models have attracted a lot of attentions recently, in particular for the linear option pricing problem. In this paper, starting with power utilities, we propose to use a martingale distortion representation of the optimal value function for the nonlinear asset allocation problem in a (non-Markovian) fractional stochastic environment (for all Hurst index $H \\in (0,1)$). We rigorously establish a first order approximation of the optimal value, where the return and volatility of the underlying asset are functions of a stationary slowly varying fractional Ornstein-Uhlenbeck process. We prove that this approximation can be also generated by a fixed zeroth order trading strategy providing an explicit strategy which is asymptotically optimal in all admissible controls. Furthermore, we extend the discussion to general utility functions, and obtain the asymptotic optimality of this fixed strategy in a specific family of admissible strategies.
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中文摘要：
粗糙随机波动率模型近年来引起了人们的广泛关注，尤其是对于线性期权定价问题。在本文中，从电力公用事业开始，我们建议在（非马尔可夫）分数随机环境中（对于所有Hurst指数$H\\In（0,1）$）使用最优值函数的鞅失真表示。我们严格建立了最优值的一阶近似值，其中基础资产的收益率和波动率是平稳缓慢变化的分数奥恩斯坦-乌伦贝克过程的函数。我们证明了这种近似也可以由一个固定的零阶交易策略生成，该策略提供了一个在所有容许控制下渐近最优的显式策略。此外，我们将讨论扩展到一般效用函数，并在一个特定的容许策略族中得到了该固定策略的渐近最优性。
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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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