Special Session 134: Mean field stochastic control problems and related topics

A Novel Approach to Pengs Maximum Principle for Mean Field SDE
Johan Benedikt Spille
Technical University Berlin
Germany
Co-Author(s):    Johan Benedikt Spille, Wilhelm Stannat
Abstract:
We present a novel approach to the proof of Peng`s maximum principle for McKean-Vlasov stochastic differential equations (SDE). The main step is the introduction of a third adjoint equation, a conditional McKean-Vlasov backward SDE, to accommodate the dualization of quadratic terms containing two independent copies of the first-order variational process. This is an intrinsic extension of the maximum principle from Peng for standard SDE and gives a conceptually consistent proof. Our approach will be useful in further extensions to the common noise setting and the infinite dimensional setting.