François Delarue - Stochastic control for large population driven by correlated noises
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 2014-04-02

François Delarue (Université de Nice)
I will discuss recent advances in large population stochastic control, in the spirit of the 
pioneering by Lasry and Lions and by Caines and Malhamé in 2006. The basic point is to seek 
approximate equilibria over families of interacting players when the number of players tends to the 
infinity, by taking benefit of some underlying propagation of chaos. The framework I will consider 
is twofold: the first one is the standard mean-field game problem, for which equilibria are 
investigated as Nash equilibria, and the second one is the control of McKean-Vlasov diffusion 
processes, for which equilibria are investigated as cooperative equilibria. In both cases, I will 
assume that players are driven by correlated noises. In this setting, I will discuss a probabilistic 
approach for proving the existence of equilibria. I will also investigate the connection with an
infinite dimensional partial differential equation, set on the space of probability measures, that 
describes the equilibria in an analytic way.
Joint work with R. Carmona and D. Lacker (Princeton).