On Information Controls

Zihao Gu; Jianfeng Zhang

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arXiv · 2602.07318

On Information Controls

Zihao Gu·Jianfeng Zhang

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Abstract

In this paper we study an optimization problem in which the control is information, more precisely, the control is a $\sigma$-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 It\^o'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.

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BibTeX RIS

Zihao Gu, Jianfeng Zhang. 2026-02-07. On Information Controls. https://arxiv.org/abs/2602.07318

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