Maximum Principle of Stochastic Optimal Control Problems with Model Uncertainty
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910909947969536 |
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| author | Hao, Tao Wen, Jiaqiang Xiong, Jie |
| author_facet | Hao, Tao Wen, Jiaqiang Xiong, Jie |
| contents | This paper is concerned with the maximum principle of stochastic optimal control problems, where the coefficients of the state equation and the cost functional are uncertain, and the system is generally under Markovian regime switching. Firstly, the $ L^β$-solutions of forward-backward stochastic differential equations with regime switching are given. Secondly, we obtain the variational inequality by making use of the continuity of solutions to variational equations with respect to the uncertainty parameter $θ$. Thirdly, utilizing the linearization and weak convergence techniques, we prove the necessary stochastic maximum principle and provide sufficient conditions for the stochastic optimal control. Finally, as an application, a risk-minimizing portfolio selection problem is studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_10454 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Maximum Principle of Stochastic Optimal Control Problems with Model Uncertainty Hao, Tao Wen, Jiaqiang Xiong, Jie Optimization and Control 93E20, 60H10 This paper is concerned with the maximum principle of stochastic optimal control problems, where the coefficients of the state equation and the cost functional are uncertain, and the system is generally under Markovian regime switching. Firstly, the $ L^β$-solutions of forward-backward stochastic differential equations with regime switching are given. Secondly, we obtain the variational inequality by making use of the continuity of solutions to variational equations with respect to the uncertainty parameter $θ$. Thirdly, utilizing the linearization and weak convergence techniques, we prove the necessary stochastic maximum principle and provide sufficient conditions for the stochastic optimal control. Finally, as an application, a risk-minimizing portfolio selection problem is studied. |
| title | Maximum Principle of Stochastic Optimal Control Problems with Model Uncertainty |
| topic | Optimization and Control 93E20, 60H10 |
| url | https://arxiv.org/abs/2309.10454 |