Title: Generalized McKean-Vlasov stochastic control problems.
Abstract: I will consider McKean-Vlasov stochastic control problems
where the cost functions and the state dynamics depend upon the joint
distribution of the controlled state and the control process. First, I
will provide a suitable version of the Pontryagin stochastic maximum
principle, showing that, in the present general framework, pointwise
minimization of the Hamiltonian with respect to the control is not a
necessary optimality condition. Then I will take a different
perspective, and present a variational approach to study a weak
formulation of such control problems, thereby establishing a new
connection between those and optimal transport problems on path space.
The talk is based on a joint project with J. Backhoff-Veraguas and R. Carmona.
- Mathematical and Computational Finance Seminar