Controlled rough SDEs, pathwise stochastic control and dynamic programming principles Article Swipe
Peter K. Friz
,
Khanh-Duy Le
,
H. Zhang
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2412.05698
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2412.05698
We study stochastic optimal control of rough stochastic differential equations (RSDEs). This is in the spirit of the pathwise control problem (Lions--Souganidis 1998, Buckdahn--Ma 2007; also Davis--Burstein 1992), with renewed interest and recent works drawing motivation from filtering, SPDEs, and reinforcement learning. Results include regularity of rough value functions, validity of a rough dynamic programming principles and new rough stability results for HJB equations, removing excessive regularity demands previously imposed by flow transformation methods. Measurable selection is used to relate RSDEs to "doubly stochastic" SDEs under conditioning. In contrast to previous works, Brownian statistics for the to-be-conditioned-on noise are not required, aligned with the "pathwise" intuition that these should not matter upon conditioning. Depending on the chosen class of admissible controls, the involved processes may also be anticipating. The resulting stochastic value functions coincide in great generality for different classes of controls. RSDE theory offers a powerful and unified perspective on this problem class.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2412.05698
- https://arxiv.org/pdf/2412.05698
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4405899347
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https://openalex.org/W4405899347Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2412.05698Digital Object Identifier
- Title
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Controlled rough SDEs, pathwise stochastic control and dynamic programming principlesWork title
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preprintOpenAlex work type
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enPrimary language
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2024Year of publication
- Publication date
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2024-12-07Full publication date if available
- Authors
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Peter K. Friz, Khanh-Duy Le, H. ZhangList of authors in order
- Landing page
-
https://arxiv.org/abs/2412.05698Publisher landing page
- PDF URL
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https://arxiv.org/pdf/2412.05698Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2412.05698Direct OA link when available
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Computer science, Dynamic programming, Control (management), Mathematical optimization, Mathematics, Artificial intelligence, AlgorithmTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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