Author:
Bouchard Bruno,Tan Xiaolu,Wang Jixin
Abstract
AbstractWe provide an Itô’s formula for $$C^1$$
C
1
-functionals of flows of conditional marginal distributions of continuous semimartingales. This is based on the notion of weak Dirichlet process, and extends the $$C^1$$
C
1
-Itô’s formula in Gozzi and Russo (Stoch Process Appl 116(11):1563–1583, 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 $$C^1$$
C
1
-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.
Publisher
Springer Science and Business Media LLC
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