SIAM Journal on Financial Mathematics, Volume 11, Issue 1, Page 240-273, January 2020.
We consider a fractional version of the Heston volatility model which is inspired by [H. Guennoun et al., SIAM J. Financial Math,, 9 (2018), pp. 1017--1045]. 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 in 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.

中文翻译：

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分数和粗糙Heston模型中的投资组合优化

SIAM金融数学杂志，第11卷，第1期，第240-273页，2020年1月。
我们考虑了由[H. Guennoun等人，SIAM J. Financial Math，9（2018），第1017--1045页]。在此模型中，我们处理电力公司功能的投资组合优化问题。使用小数部分的适当表示，然后进行合理的近似，我们表明可以在经典的随机控制框架中提出问题。这种方法对于分数过程是通用的。我们得出明确的解决方案，并获得综合波动率的拉普拉斯变换作为副产品。为了摆脱一些不良的特征，我们引入了一种基于Marchaud分数导数的粗糙路径场景新模型。我们提供了一个数值研究来强调我们的结果。