Section: New Results
The mathematical modeling of default contagion, by which an economic shock causing initial losses and default of a few institutions is amplified due to complex linkages, leading to large scale defaults, can be addressed by various techniques, such as network approaches (see in particular  ), or mean field interaction models  ,  . Little has been done so far on the control of such systems and A. Sulem has started to contribute on these issues in the framework of random graph models in collaboration with A. Minca (Cornell University) and H. Amini (EPFL). In  ,  , they consider a financial network described as a weighted directed graph, in which nodes represent financial institutions and edges the exposures between them. Here, the distress propagation is modeled as an epidemics on this graph. They study the optimal intervention of a lender of last resort who seeks to make equity infusions in a banking system prone to insolvency and to bank runs, under complete and incomplete information of the failure cluster, in order to minimize the contagion effects.
R. Elie is studying risk systemic propagation and its links with mean field games.