A local maximum principle for robust optimal control problems of quadratic BSDEs
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909072303849472 |
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| author | Hao, Tao Wen, Jiaqiang Zhang, Qi |
| author_facet | Hao, Tao Wen, Jiaqiang Zhang, Qi |
| contents | The paper concerns the necessary maximum principle for robust optimal control problems of quadratic BSDEs. The coefficient of the systems depends on the parameter $θ$, and the generator of BSDEs is of quadratic growth in $z$. Since the model is uncertain, the variational inequality is proved by weak convergence technique. In addition, due to the generator being quadratic with respect to $z$, the forward adjoint equations are SDEs with unbounded coefficient involving mean oscillation martingales. Using reverse Hölder inequality and John-Nirenberg inequality, we show that its solutions are continuous with respect to the parameter $θ$. The necessary and sufficient conditions for robust optimal control are proved by linearization method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07029 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A local maximum principle for robust optimal control problems of quadratic BSDEs Hao, Tao Wen, Jiaqiang Zhang, Qi Optimization and Control 93E20, 60H10 The paper concerns the necessary maximum principle for robust optimal control problems of quadratic BSDEs. The coefficient of the systems depends on the parameter $θ$, and the generator of BSDEs is of quadratic growth in $z$. Since the model is uncertain, the variational inequality is proved by weak convergence technique. In addition, due to the generator being quadratic with respect to $z$, the forward adjoint equations are SDEs with unbounded coefficient involving mean oscillation martingales. Using reverse Hölder inequality and John-Nirenberg inequality, we show that its solutions are continuous with respect to the parameter $θ$. The necessary and sufficient conditions for robust optimal control are proved by linearization method. |
| title | A local maximum principle for robust optimal control problems of quadratic BSDEs |
| topic | Optimization and Control 93E20, 60H10 |
| url | https://arxiv.org/abs/2401.07029 |