Optimal investment strategies with derivative trading under 4/2-CIR jump-diffusion stochastic hybrid models

This paper investigates the continuous-time optimal investment strategy for a constant relative risk aversion investor under a novel stochastic hybrid framework: The 4/2-Cox-Ingersoll-Ross (CIR) jump-diffusion stochastic hybrid model. The financial market comprises a money market account, a zero-coupon bond, a stock index, and stock derivatives. Explicit solutions for the optimal strategy are derived using stochastic optimal control theory and the associated Hamilton-Jacobi-Bellman equation under a power utility function. Additionally, we characterize the optimal risk exposure, quantify the suboptimal strategy, and compute the associated utility loss within the 4/2-CIR jump-diffusion stochastic hybrid model. Numerical experiments analyze the impact of key portfolio model parameters on the optimal risk exposure and utility loss. Our results demonstrate that the risk aversion coefficient, investment horizon, equity risk premium, volatility risk premium, interest rate risk premium, and jump intensity significantly influence the optimal risk exposure. Furthermore, the short-sighted losses increase with positive risk premium factors and decrease with negative ones. Crucially, investment decisions derived under the proposed 4/2-CIR jump-diffusion stochastic hybrid model outperform those based on existing 4/2 stochastic volatility and 4/2-CIR stochastic hybrid models.