Portfolio optimisation under rough Heston models

TL;DR

This thesis explores portfolio optimization under non-Markovian rough Heston models using two approaches, deriving semi-closed form solutions and comparing their effectiveness, contributing to advanced financial modeling with rough volatility.

Contribution

Introduces two novel methods for solving portfolio optimization under rough Heston models, including auxiliary processes and finite-dimensional approximations, extending classical results to complex rough volatility settings.

Findings

Optimal strategies derived in semi-closed form

Comparison of two different solution approaches

Framework adaptable to complex financial markets

Abstract

This thesis investigates Merton's portfolio problem under two different rough Heston models, which have a non-Markovian structure. The motivation behind this choice of problem is due to the recent discovery and success of rough volatility processes. The optimisation problem is solved from two different approaches: firstly by considering an auxiliary random process, which solves the optimisation problem with the martingale optimality principle, and secondly, by a finite dimensional approximation of the volatility process which casts the problem into its classical stochastic control framework. In addition, we show how classical results from Merton's portfolio optimisation problem can be used to help motivate the construction of the solution in both cases. The optimal strategy under both approaches is then derived in a semi-closed form, and comparisons between the results made. The approaches discussed in this thesis, combined with the historical works on the distortion transformation, provide a strong foundation to build models capable of handling increasing complexity demanded by the ever growing financial market.