Robust Stochastic Games and Systemic Risk

30 Pages Posted: 24 Aug 2017

See all articles by Xuancheng Huang

Xuancheng Huang

University of Toronto

Sebastian Jaimungal

University of Toronto - Department of Statistics

Date Written: August 22, 2017

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

Suggested Citation

Huang, Xuancheng and Jaimungal, Sebastian, Robust Stochastic Games and Systemic Risk (August 22, 2017). Available at SSRN: https://ssrn.com/abstract=3024021 or http://dx.doi.org/10.2139/ssrn.3024021

Xuancheng Huang (Contact Author)

University of Toronto ( email )

Toronto, Ontario M5S 3G8
Canada

Sebastian Jaimungal

University of Toronto - Department of Statistics ( email )

100 St. George St.
Toronto, Ontario M5S 3G3
Canada

HOME PAGE: http://http:/sebastian.statistics.utoronto.ca

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