This paper investigates Merton's portfolio problem in a rough stochastic environment described by Volterra Heston model. The model has a non-Markovian and non-semimartingale structure. By considering an auxiliary random process, we solve the portfolio optimization problem with the martingale optimality principle. The optimal strategy is derived in a semi-closed form that depends on the solution of a Riccati-Volterra equation. Numerical studies suggest that investment demand decreases with the roughness of the market.
↧