It\^o-Wentzell formulas for semimartingale conditional laws with applications to mean-field control

Nizar Touzi; Mehdi Talbi

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arXiv · 2510.00242

It\^o-Wentzell formulas for semimartingale conditional laws with applications to mean-field control

Nizar Touzi·Mehdi Talbi

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Abstract

The present paper is an extension of Fadle-Touzi (2024). Following the same methodology, merely based on Taylor expansions, we establish the It\^o and It\^o-Wentzell formulae for flows of conditional distributions of general semimartingales, thus allowing for discontinuous semimartingales with possibly discontinuous flows of conditional marginals. We apply these results to derive the dynamic programming equations corresponding to mean field control problems with Poisson type common noise and mean field stopping problems with common noise.

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Nizar Touzi, Mehdi Talbi. 2025-09-30. It\^o-Wentzell formulas for semimartingale conditional laws with applications to mean-field control. https://arxiv.org/abs/2510.00242

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