🤖 AI Summary
This study addresses the continuous-time Markowitz mean–variance portfolio selection problem in a multidimensional affine Volterra market characterized by unbounded stochastic coefficients, non-Markovian dynamics, and non-semimartingale structure—settings where classical methods fail. For the first time in such a rough framework, the authors construct stochastic factor solutions to a Riccati-type backward stochastic differential equation and derive closed-form expressions for both the optimal feedback strategy and the efficient frontier via a multidimensional Riccati–Volterra equation. By integrating affine Volterra processes with numerical simulations of the rough Heston model, the approach reveals the pronounced impact of volatility roughness and stochastic correlation on optimal investment decisions, thereby providing a novel analytical toolkit for non-Markovian mean–variance optimization.
📝 Abstract
We investigate the continuous-time Markowitz mean-variance portfolio selection problem within a multivariate class of fake stationary affine Volterra models. In this non-Markovian and non-semimartingale market framework with unbounded random coefficients, the classical stochastic control approach cannot be directly applied to the associated optimization task. Instead, the problem is tackled using a stochastic factor solution to a Riccati backward stochastic differential equation (BSDE). The optimal feedback control is characterized by means of this equation, whose explicit solutions is derived in terms of multi-dimensional Riccati-Volterra equations. Specifically, we obtain analytical closed-form expressions for the optimal portfolio policies as well as the mean-variance efficient frontier, both of which depend on the solution to the associated multivariate Riccati-Volterra system. To illustrate our results, numerical experiments based on a two dimensional fake stationary rough Heston model highlight the impact of rough volatilities and stochastic correlations on the optimal Markowitz strategies.