A $C^1$-It\^o's formula for flows of semimartingale distributions
Probability
2024-04-30 v3
Abstract
We provide an It\^o's formula for -functionals of flows of conditional marginal distributions of continuous semimartingales. This is based on the notion of weak Dirichlet process, and extends the -It\^o's formula in Gozzi and Russo (2006) to this context. As the first application, we study a class of McKean-Vlasov optimal control problems, and establish a verification theorem which only requires -regularity of its value function, which is equivalently the (viscosity) solution of the associated HJB master equation. It goes together with a novel duality result.
Keywords
Cite
@article{arxiv.2307.07165,
title = {A $C^1$-It\^o's formula for flows of semimartingale distributions},
author = {Bruno Bouchard and Xiaolu Tan and Jixin Wang},
journal= {arXiv preprint arXiv:2307.07165},
year = {2024}
}