Causal Hamilton-Jacobi-Bellman Equations for Anticipative Stochastic Optimal Control
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909826576023552 |
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| author | Bank, Peter Bielert, Franziska |
| author_facet | Bank, Peter Bielert, Franziska |
| contents | We consider a stochastic optimal control problem where the controller can anticipate the evolution of the driving noise over some dynamically changing time window. The controlled state dynamics are understood as a rough differential equation. We combine the martingale optimality principle with a functional form of Itô's formula to derive a Hamilton-Jacobi-Bellman (HJB) equation for this problem. This HJB equation is formulated in terms of Dupire's functional derivatives and involves a transport equation arising from the anticipativity of the problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08657 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Causal Hamilton-Jacobi-Bellman Equations for Anticipative Stochastic Optimal Control Bank, Peter Bielert, Franziska Optimization and Control 93E20, 60L90, 35R15 We consider a stochastic optimal control problem where the controller can anticipate the evolution of the driving noise over some dynamically changing time window. The controlled state dynamics are understood as a rough differential equation. We combine the martingale optimality principle with a functional form of Itô's formula to derive a Hamilton-Jacobi-Bellman (HJB) equation for this problem. This HJB equation is formulated in terms of Dupire's functional derivatives and involves a transport equation arising from the anticipativity of the problem. |
| title | Causal Hamilton-Jacobi-Bellman Equations for Anticipative Stochastic Optimal Control |
| topic | Optimization and Control 93E20, 60L90, 35R15 |
| url | https://arxiv.org/abs/2507.08657 |