Portfolio optimization in signature-based models

This work investigates portfolio optimization within a model belonging to a class of models becoming increasingly popular in financial modelling literature: signature-based ones. In particular, the model analyzed represents market volatility through the use of "path signatures". The portfolio optimization problem, formulated as a mean-variance problem in continuous time, is addressed through the use of reinforcement learning algorithms recently developed in the literature. The efficacy of the RL algorithm is validated against a simple geometric Brownian motion and the signature-based model, showing the challenges of optimizing portfolios under complex stochastic environments. Numerical simulations and scenario analysis demonstrate the ability of the framework to achieve robust portfolio performance in varying market conditions.