Abstract:
In this talk, we consider an optimal control problem for a conditioned process. This model was first introduced by P.-L. Lions in his lectures at College de France. When the optimization is done over controls of feedback type (i.e., depending only on the state of the process), the optimal solution can be characterized by a system of two partial differential equations of mean field type: a forward (Fokker- Planck) equation and a backward (Hamilton-Jacobi-Bellman) equation, both with Dirichlet boundary conditions. They describe respectively the evolution of the distribution and of the value function. We also consider a problem arising in the long time asymptotics. This is a control problem driven by the principal eigenvalue problem associated with a Fokker-Planck equation with Dirichlet condition. We study in details particular aspects of the theory and discuss numerical results. This is a joint work with Yves Achdou (University Paris-Diderot).
Biography:
Mathieu Laurière is a Postdoctoral Research Associate at Princeton university (ORFE).
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai