英文标题：
《Portfolio Optimization in Fractional and Rough Heston Models》
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作者：
Nicole B\\\"auerle, Sascha Desmettre
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最新提交年份：
2019
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英文摘要：
We consider a fractional version of the Heston volatility model which is inspired by [16]. Within this model we treat portfolio optimization problems for power utility functions. Using a suitable representation of the fractional part, followed by a reasonable approximation we show that it is possible to cast the problem into the classical stochastic control framework. This approach is generic for fractional processes. We derive explicit solutions and obtain as a by-product the Laplace transform of the integrated volatility. In order to get rid of some undesirable features we introduce a new model for the rough path scenario which is based on the Marchaud fractional derivative. We provide a numerical study to underline our results.
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中文摘要：
我们考虑了Heston波动率模型的一个分数版本，其灵感来自【16】。在这个模型中，我们处理电力效用函数的投资组合优化问题。使用分数部分的适当表示，然后进行合理的近似，我们表明可以将问题转换为经典的随机控制框架。这种方法适用于分数过程。我们推导出显式解，并作为副产品获得积分波动率的拉普拉斯变换。为了消除一些不良特征，我们引入了一种新的基于Marchaud分数阶导数的粗糙路径模型。我们提供了一个数值研究来强调我们的结果。
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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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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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