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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.07318 |
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| _version_ | 1866908919987699712 |
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| author | Gu, Zihao Zhang, Jianfeng |
| author_facet | Gu, Zihao Zhang, Jianfeng |
| contents | In this paper we study an optimization problem in which the control is information, more precisely, the control is a $σ$-algebra or a filtration. In a dynamic setting, we establish the dynamic programming principle and the law invariance of the value function. The latter requires a condition slightly stronger than the (H)-hypothesis for the admissible filtration, and enables us to define the value function on $\mathcal P_2(\mathcal P_2(\mathbb R^d))$, the space of laws of random probability measures. By using a new Itô's formula for smooth functions on $\mathcal P_2(\mathcal P_2(\mathbb R^d))$, we characterize the value function of the information control problem by an Hamilton-Jacobi-Bellman equation on this space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07318 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Information Controls Gu, Zihao Zhang, Jianfeng Optimization and Control 35R15, 49N30, 60H30, 91A27 In this paper we study an optimization problem in which the control is information, more precisely, the control is a $σ$-algebra or a filtration. In a dynamic setting, we establish the dynamic programming principle and the law invariance of the value function. The latter requires a condition slightly stronger than the (H)-hypothesis for the admissible filtration, and enables us to define the value function on $\mathcal P_2(\mathcal P_2(\mathbb R^d))$, the space of laws of random probability measures. By using a new Itô's formula for smooth functions on $\mathcal P_2(\mathcal P_2(\mathbb R^d))$, we characterize the value function of the information control problem by an Hamilton-Jacobi-Bellman equation on this space. |
| title | On Information Controls |
| topic | Optimization and Control 35R15, 49N30, 60H30, 91A27 |
| url | https://arxiv.org/abs/2602.07318 |