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 roughnessof the market .
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. Optimal strategies for power and exponential utilities are derived in semi-closed form solutions depending on the respective Riccati-Volterra equations. We numerically examine the relationship between investment demand and volatility roughness .
R
The optimal strategy is derived in a
Optimal strategies for power and exponential utilities are derived in
R
that depends on the solution of a
solutions depending on the respective
R
equation. Numerical studies suggest that investment demand decreases with the roughnessof the market
equations. We numerically examine the relationship between investment demand and volatility roughness