Title: Portfolio Optimization in Fractional and Rough Heston Models,
Abstract: 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.