报告题目：Itô's formula for flows of measures on semimartingales

报告人：魏晓利 教授  哈尔滨工业大学

报告时间：12月25日  上午10:00-11:00

报告地点：管理楼1418

摘要：

We establish Itô's formula along flows of probability measures associated with general semimartingales; this generalizes existing results for flows of measures on Itô processes. Our approach is to first establish Itô's formula for cylindrical functions and then extend it to the general case via function approximation and localization techniques.

This general form of Itô's formula enables the derivation of dynamic programming equations and verification theorems for McKean--Vlasov controls with jump diffusions and for McKean--Vlasov mixed regular-singular control problems. It also allows for generalizing the classical relationship between the maximum principle and the dynamic programming principle to the McKean--Vlasov singular control setting, where the adjoint process is expressed in terms of the derivative of the value function with respect to the probability measures. This is a joint work with Xin Guo and Huyên Pham.