Abstract
We establish the existence and uniqueness of viscosity solutions to the weakly coupled second-order parabolic Hamilton–Jacobi–Bellman equations under Hölder continuous condition, for which the standard quasi-monotone condition does not hold. The existence theorem is established by solving the finite horizon optimal control problem for regime-switching stochastic processes with Hölder continuous coefficients such as the Cox–Ingersoll–Ross process. A comparison principle for this weakly coupled system without state constraint is established.
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Li, J., Shao, J. Wellposedness of Viscosity Solutions to Weakly Coupled HJB Equations Under Hölder continuous conditions. Appl Math Optim 87, 31 (2023). https://doi.org/10.1007/s00245-022-09946-0
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DOI: https://doi.org/10.1007/s00245-022-09946-0