Relationship between stochastic maximum principle and dynamic programming principle under convex expectation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913503849218048 |
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| author | Li, Xiaojuan Hu, Mingshang |
| author_facet | Li, Xiaojuan Hu, Mingshang |
| contents | In this paper, we study the relationship between maximum principle (MP) and dynamic programming principle (DPP) for forward-backward control system under consistent convex expectation dominated by G-expectation. Under the smooth assumptions for the value function, we get the relationship between MP and DPP under a reference probability by establishing a useful estimate. If the value function is not smooth, then we obtain the first-order sub-jet and super-jet of the value function at any t. However, the processing method in this case is much more difficult than that when t equals 0. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10987 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relationship between stochastic maximum principle and dynamic programming principle under convex expectation Li, Xiaojuan Hu, Mingshang Optimization and Control 93E20, 60H10, 35K15 In this paper, we study the relationship between maximum principle (MP) and dynamic programming principle (DPP) for forward-backward control system under consistent convex expectation dominated by G-expectation. Under the smooth assumptions for the value function, we get the relationship between MP and DPP under a reference probability by establishing a useful estimate. If the value function is not smooth, then we obtain the first-order sub-jet and super-jet of the value function at any t. However, the processing method in this case is much more difficult than that when t equals 0. |
| title | Relationship between stochastic maximum principle and dynamic programming principle under convex expectation |
| topic | Optimization and Control 93E20, 60H10, 35K15 |
| url | https://arxiv.org/abs/2409.10987 |