Robust Stochastic Games and Systemic Risk

Abstract

Interbank borrowing and lending may induce systemic risk into financial markets. A simple model of this is to assume that log-monetary reserves are coupled, and that banks can also borrow/lend from/to a central bank. When all banks optimize their cost of borrowing and lending, this leads to a stochastic game which, as Carmona et al. (2015) show, induces some stability in the market. All models, however, have error in them, and here we account for model uncertainty (aka, ambiguity aversion) by recasting the problem as a robust stochastic game. We succeed in providing a strategy which leads to a Nash equilibria for the finite game, and also study the mean-field game limit. To this end, we prove that an -Nash equilibrium exists, and a verification theorem is shown to hold for convex-concave cost functions. Moreover, we show that when firms are ambiguity-averse, default probabilities can be reduced relative to their ambiguity-neutral counterparts.

Keywords: Interbank Borrowing and Lending, Mean-Field Games, Nash Equilibrium, Stochastic Games, Model Uncertainty, Ambiguity Aversion

JEL Classification: C60, C61, C63, C70, C73, G01, G10, G20, G21