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Mean Field Games and Systemic Risk

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  • Rene Carmona
  • Jean-Pierre Fouque
  • Li-Hsien Sun

Abstract

We propose a simple model of inter-bank borrowing and lending where the evolution of the log-monetary reserves of $N$ banks is described by a system of diffusion processes coupled through their drifts in such a way that stability of the system depends on the rate of inter-bank borrowing and lending. Systemic risk is characterized by a large number of banks reaching a default threshold by a given time horizon. Our model incorporates a game feature where each bank controls its rate of borrowing/lending to a central bank. The optimization reflects the desire of each bank to borrow from the central bank when its monetary reserve falls below a critical level or lend if it rises above this critical level which is chosen here as the average monetary reserve. Borrowing from or lending to the central bank is also subject to a quadratic cost at a rate which can be fixed by the regulator. We solve explicitly for Nash equilibria with finitely many players, and we show that in this model the central bank acts as a clearing house, adding liquidity to the system without affecting its systemic risk. We also study the corresponding Mean Field Game in the limit of large number of banks in the presence of a common noise.

Suggested Citation

  • Rene Carmona & Jean-Pierre Fouque & Li-Hsien Sun, 2013. "Mean Field Games and Systemic Risk," Papers 1308.2172, arXiv.org.
  • Handle: RePEc:arx:papers:1308.2172
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    Cited by:

    1. Marcel Nutz, 2016. "A Mean Field Game of Optimal Stopping," Papers 1605.09112, arXiv.org, revised Nov 2017.
    2. RĂ©gis Chenavaz & Corina Paraschiv & Gabriel Turinici, 2017. "Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach," Working Papers hal-01592958, HAL.
    3. Lacker, Daniel, 2015. "Mean field games via controlled martingale problems: Existence of Markovian equilibria," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2856-2894.
    4. Philippe Casgrain & Sebastian Jaimungal, 2018. "Algorithmic Trading with Partial Information: A Mean Field Game Approach," Papers 1803.04094, arXiv.org.

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