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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.11523 |
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| _version_ | 1866917250127101952 |
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| author | Ding, Kai Li, Xun Lv, Siyu Zhang, Xin |
| author_facet | Ding, Kai Li, Xun Lv, Siyu Zhang, Xin |
| contents | This paper is concerned with a discounted stochastic optimal control problem for regime switching diffusion in an infinite horizon. First, as a preliminary with particular interests in its own right, the global well-posedness of infinite horizon forward and backward stochastic differential equations with Markov chains and the asymptotic property of their solutions when time goes to infinity are obtained. Then, a sufficient stochastic maximum principle for optimal controls is established via a dual method under certain convexity condition of the Hamiltonian. As an application of our maximum principle, a linear quadratic production planning problem is solved with an explicit feedback optimal production rate. The existence and uniqueness of a non-negative solution to the associated algebraic Riccati equation are proved. Numerical experiments are reported to illustrate the theoretical results, especially, the monotonicity of the value function on various model parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11523 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An infinite horizon sufficient stochastic maximum principle for regime switching diffusions and applications Ding, Kai Li, Xun Lv, Siyu Zhang, Xin Optimization and Control This paper is concerned with a discounted stochastic optimal control problem for regime switching diffusion in an infinite horizon. First, as a preliminary with particular interests in its own right, the global well-posedness of infinite horizon forward and backward stochastic differential equations with Markov chains and the asymptotic property of their solutions when time goes to infinity are obtained. Then, a sufficient stochastic maximum principle for optimal controls is established via a dual method under certain convexity condition of the Hamiltonian. As an application of our maximum principle, a linear quadratic production planning problem is solved with an explicit feedback optimal production rate. The existence and uniqueness of a non-negative solution to the associated algebraic Riccati equation are proved. Numerical experiments are reported to illustrate the theoretical results, especially, the monotonicity of the value function on various model parameters. |
| title | An infinite horizon sufficient stochastic maximum principle for regime switching diffusions and applications |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2506.11523 |