Portfolio Optimization in Fractional and Rough Heston Models

TL;DR

This paper develops a fractional and rough Heston model for portfolio optimization, deriving explicit solutions and providing numerical analysis to address challenges in modeling volatility with fractional processes.

Contribution

It introduces a novel fractional Heston model and a new rough path model based on Marchaud derivatives, with explicit solutions for portfolio optimization.

Findings

Explicit solutions for fractional Heston portfolio optimization

Laplace transform of integrated volatility derived

Numerical results support the models' effectiveness

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.