### Robust Stochastic Games and Systemic Risk

Sebastian Jaimungal
Department of Statistical Sciences and Mathematical Finance Program University of Toronto

May 24, 2017 at  2:30 PM
McConnell Engineering Room 603

Interbank borrowing and lending may induce systemic risk into financial markets. To incorporate this effect, log-monetary reserves must be coupled. When, banks borrow/lend from/to a central bank, and they optimize their cost of borrowing and lending in a stochastic game setting, Carmona et. al. (2015) show that market stability can be increased. Their results follow from a specific modelling framework. All models, however, have error in them, and here we account for model uncertainty (also known as ambiguity aversion) by recasting the problem as a robust stochastic game. By proving a robust variation of the stochastic Pontryagin maximum principle, we succeed in providing a strategy which leads to a Nash equilibria for the finite game, and also study the mean-field game limit. We further prove that an $\epsilon$-Nash equilibrium exists, and a verification theorem is shown to hold for more general convex-concave cost functions. Moreover, we show that when firms are ambiguity-averse, default probabilities can be reduced relative to their ambiguity-neutral counterparts.