|Date: Wednesday, January 05, 2022
Location: Zoom Virtual (4:00 PM to 5:00 PM)
Title: Dynamic programming equation for the mean field optimal stopping problem
Abstract: We study the optimal stopping problem of McKean-Vlasov diffusions when the criterion is a function of the law of the stopped process. A remarkable new feature in this setting is that the stopping time also impacts the dynamics of the stopped process through the dependence of the coefficients on the law. The mean field stopping problem is introduced in weak formulation in terms of the joint marginal law of the stopped underlying process and the survival process. This formulation satisfies a dynamic programming principle. The corresponding dynamic programming equation is an obstacle problem on the Wasserstein space, and is obtained by means of a general Itô's formula for flows of marginal laws of càdlàg semimartingales. We introduce a notion of viscosity solutions for this equation, which satisfies the properties of stability and comparison. We also provide a finite-dimensional approximation, which is closely related to the multiple optimal stopping problem.
Speaker: Mehdi Talbi
Institution: Ecole Poytechnique