Fully Coupled Nonlinear FBS$\Delta$Es: Solvability and LQ Control Insights
| Autor: | Niu, Zhipeng, Meng, Qingxin, Li, Xun, Tang, Maoning |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | This paper explores a class of fully coupled nonlinear forward-backward stochastic difference equations (FBS$\Delta$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$\Delta$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$\Delta$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. Comment: arXiv admin note: text overlap with arXiv:2310.13195 |
| Databáze: | arXiv |
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