  Motivated by empirical evidence for rough volatility models, this paper
investigates continuous-time mean-variance (MV) portfolio selection under the
Volterra Heston model. Due to the non-Markovian and non-semimartingale nature
of the model, classic stochastic optimal control frameworks are not directly
applicable to the associated optimization problem. By constructing an auxiliary
stochastic process, we obtain the optimal investment strategy, which depends on
the solution to a Riccati-Volterra equation. The MV efficient frontier is shown
to maintain a quadratic curve. Numerical studies show that both roughness and
volatility of volatility materially affect the optimal strategy.
