Wellposedness of Viscosity Solutions to Weakly Coupled HJB Equations Under Hölder continuous conditions

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...

Full description

Saved in:
Bibliographic Details
Published in:Applied mathematics & optimization 2023-04, Vol.87 (2), p.31, Article 31
Main Authors: Li, Jianrui, Shao, Jinghai
Format: Article
Language:English
Subjects:
Applied mathematics
Calculus of Variations and Optimal Control
Optimization
Control
Dynamic programming
Existence theorems
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Optimal control
Optimization
Partial differential equations
Simulation
Stochastic models
Stochastic processes
Systems Theory
Theoretical
Utility functions
Viscosity
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-022-09946-0