Dynamic optimal control for distress large financial networks and Mean field systems with jumps.

Summary This thesis proposes models and methods to study risk control in large financial systems. In the first part, we propose a structural approach: we consider a financial system represented as a network of institutions connected to each other by strategic interactions that are sources of funding but also by interactions that expose them to default contagion risk. The novelty of our approach lies in the fact that these two types of interactions interfere. We propose new notions of equilibrium for these systems and study the optimal connectivity of the network and the associated systemic risk. In a second part, we introduce systemic risk measures defined by backward stochastic differential equations directed by mean-field operators and study associated optimal stopping problems. The last part deals with optimal portfolio liquidation issues.