Portfolio optimization based on exponential utility criterion in the fractional and rough Heston models

Portfolio optimization is one of the hot issues in financial theory research. In this paper, we study portfolio optimization in the fractional and rough Heston models. When the price process of the risky asset satisfies the fractional or rough Heston model and the goal is to maximize the expected exponential utility of investors, the original optimization problem is transformed into a classical optimization problem under the approximation model by the finite-dimensional approximation of volatility, so that the corresponding Hamilton-Jacobi-Bellman equation is established by using stochastic dynamic programming principle. In addition, the explicit expressions for the value function of the approximate optimization problem and the optimal portfolio strategy are derived, and the convergence of the approximate model is proved. Finally, the characteristics of the fractional and rough Heston models are compared by numerical methods, and the study shows that the fractional Heston model is applicable to short-term investment horizon and the rough Heston model is applicable to long-term investment horizon, and the sensitivity of the investment strategy process and the wealth process with regard to parameters is analyzed.