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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.01749 |
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| _version_ | 1866908473615187968 |
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| author | Niu, Zhipeng Meng, Qingxin Li, Xun Tang, Maoning |
| author_facet | Niu, Zhipeng Meng, Qingxin Li, Xun Tang, Maoning |
| contents | This paper explores a class of fully coupled nonlinear forward-backward stochastic difference equations (FBS$Δ$Es). Building on insights from linear quadratic optimal control problems, we introduce a more relaxed framework of domination-monotonicity conditions specifically designed for discrete systems. Utilizing these conditions, we apply the method of continuation to demonstrate the unique solvability of the fully coupled FBS$Δ$Es and derive a set of solution estimates. Moreover, our results have considerable implications for various related linear quadratic (LQ) problems, particularly where stochastic Hamiltonian systems are aligned with the FBS$Δ$Es meeting these introduced domination-monotonicity conditions. As a result, solving the associated stochastic Hamiltonian systems allows us to derive explicit expressions for the unique optimal controls. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01749 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fully Coupled Nonlinear FBS$Δ$Es: Solvability and LQ Control Insights Niu, Zhipeng Meng, Qingxin Li, Xun Tang, Maoning Optimization and Control This paper explores a class of fully coupled nonlinear forward-backward stochastic difference equations (FBS$Δ$Es). Building on insights from linear quadratic optimal control problems, we introduce a more relaxed framework of domination-monotonicity conditions specifically designed for discrete systems. Utilizing these conditions, we apply the method of continuation to demonstrate the unique solvability of the fully coupled FBS$Δ$Es and derive a set of solution estimates. Moreover, our results have considerable implications for various related linear quadratic (LQ) problems, particularly where stochastic Hamiltonian systems are aligned with the FBS$Δ$Es meeting these introduced domination-monotonicity conditions. As a result, solving the associated stochastic Hamiltonian systems allows us to derive explicit expressions for the unique optimal controls. |
| title | Fully Coupled Nonlinear FBS$Δ$Es: Solvability and LQ Control Insights |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2410.01749 |