This paper develops a robust portfolio selection framework under a double Heston stochastic volatility model with ambiguity aversion, and proposes a hybrid framework that combines the Extended Kalman Filter (EKF) with an LSTM neural network for policy approximation. Under an explicit parameter restriction, we derive closed-form solutions for the optimal portfolio exposures and worst-case probability measures for a constant relative risk aversion investor who exhibits aversion to model ambiguity across both volatility components and stock return drivers. The Hamilton–Jacobi–Bellman equation is solved explicitly, yielding Riccati equations with analytical solutions under parameter conditions ensuring well-posedness. A rigorous verification theorem confirms optimality and uniqueness within a class of admissible controls subject to the attainability constraint induced by the structural singularity of the exposure matrix. To address the practical challenge of unobservable volatility states, we implement an EKF for sequential state estimation, followed by an LSTM network that learns the mapping from observable technical indicators and filtered volatility estimates to optimal portfolio exposures. Numerical simulations calibrated to Intel Corporation data demonstrate that the double Heston model generates superior wealth accumulation compared to single-factor alternatives, with the LSTM achieving high tracking accuracy of the exact Hamilton–Jacobi–Bellman solution.
