2025/07/27 by Qian Qi, Qi, Qian
Computer Science · Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Probability (math.PR) #Quantum chaos and dynamical systems #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2507.20353
openalex publication_date 2025/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
We derive a new class of non-linear expectations from first-principles deterministic chaotic dynamics. The homogenization of the system's skew-adjoint microscopic generator is achieved using the spectral theory of transfer operators for uniformly hyperbolic flows. We prove convergence in the viscosity sense to a macroscopic evolution governed by a fully non-linear Hamilton-Jacobi-Bellman (HJB) equation. Our central result establishes that the HJB Hamiltonian possesses a rigid structure: affine in the Hessian but demonstrably non-convex in the gradient. This defines a new θ-expectation and constructively establishes a class of non-convex stochastic control problems fundamentally outside the sub-additive framework of G-expectations.