# Mean Field Games and Systemic Risk

@article{Carmona2013MeanFG, title={Mean Field Games and Systemic Risk}, author={Ren{\'e} A. Carmona and Jean-Pierre Fouque and Li-Hsien Sun}, journal={ERN: Other Game Theory \& Bargaining Theory (Topic)}, year={2013} }

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… Expand

#### 197 Citations

Systemic Risk and Interbank Lending

- Mathematics, Economics
- J. Optim. Theory Appl.
- 2018

A simple model of the banking system incorporating a game feature, where the evolution of monetary reserve is modeled as a system of coupled Feller diffusions, which leads to a flocking effect implying stability or systemic risk depending on the level of the growth rate. Expand

Systemic Risk and Stochastic Games with Delay

- Computer Science, Economics
- J. Optim. Theory Appl.
- 2018

A model of inter-bank lending and borrowing which takes into account clearing debt obligations is proposed and an open-loop Nash equilibrium is obtained using a system of fully coupled forward and advanced-backward stochastic differential equations. Expand

STABILITY IN A MODEL OF INTER-BANK LENDING

- 2013

We propose a simple model of the banking system and analyze stochastic stability of inter-bank lending. The monetary reserves of banks are modeled as a system of interacting Feller diffusions. The… Expand

Systemic Risk and Heterogeneous Mean Field Type Interbank Network

- Mathematics
- 2019

We study the system of heterogeneous interbank lending and borrowing based on the relative average of log-capitalization given by the linear combination of the average within groups and the ensemble… Expand

Centralized systemic risk control in the interbank system: weak formulation and Gamma-convergence

- Mathematics, Economics
- 2021

This paper studies a systemic risk control problem by the central bank, which dynamically plans monetary supply for the interbank system with borrowing and lending activities. Facing both… Expand

Centralized systemic risk control in the interbank system: Relaxed control and Gamma-convergence

- Mathematics
- 2021

This paper studies a systemic risk control problem by the central bank, which dynamically plans monetary supply for the interbank system with borrowing and lending activities. Facing both… Expand

Financial Asset Bubbles in Banking Networks

- Economics, Computer Science
- SIAM J. Financial Math.
- 2019

We consider a banking network represented by a system of stochastic differential equations coupled by their drift. We assume a core-periphery structure, and that the banks in the core hold a bubbly… Expand

Stability in a Model of Interbank Lending

- Computer Science, Economics
- SIAM J. Financial Math.
- 2013

The model is simple enough for mathematical analysis, yet captures how lending preferences of banks affect possible multiple bank failures, and quantifies the lending preference from one bank to another as a function of all the reserves. Expand

Financial Asset Bubbles in Banking Networks \ast

- 2019

We consider a banking network represented by a system of stochastic differential equations coupled by their drift. We assume a core-periphery structure, where banks in the core hold a bubbly asset.… Expand

Systemic risk governance in a dynamical model of a banking system

- Economics, Mathematics
- J. Glob. Optim.
- 2019

The governance of systemic risk in a banking system model based on the choice of the log-monetary reserves of a kind of “ideal bank” as a function of time and on the solution of an optimal control problem for the mean field approximation of the Banking system model is presented. Expand

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Stability in a Model of Interbank Lending

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