Motivated by empirical evidence for rough volatility models, this paper investigates the continuous-time mean-variance (MV) portfolio selection under 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 that 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 affect the optimal strategy materially.
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