Mean Field Games and Systemic Risk

By René A. Carmona, Jean-Pierre Fouque 3, Li-Hsien Sun. 2013

323 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/b61d24eaf15aa5f00d8d51ee182029360dd605a5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Finance

Citations in the corpus

Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications (2016, unknown): “W 0, called idiosyncratic noises, ρ(It) ∈ [−1, 1] is the correlation between the idiosyncratic noise and the common noise, κ(It) ≥ 0 is the rate of mean-reversion in the interaction from borrowing and lending between the banks, σ(It) > 0 is the volatility of the bank reserves, and compared to the or”
The Master equation in mean field theory (2014, unknown): “ 2 (y −x)2, g(x,m,v) = α(y −x)+v, h(x,m) = c 2 (y −x)2. (7.4) It is then easy to check that H(x,m,q) = µ−λ2 2 (y −x)2 +q(α +λ)(y −x)− 1 2 q2, and G(x,m,q) = (α +λ)(y −x) −q. 35 To preserve convexity, [5] assume that µ−λ2 > 0. The Master equation (4.6) under this setting becomes ”
$N$-player games and mean-field games with absorption (2016, background): “There, the players can be interpreted as interacting firms striving to maximize some objective functional, for instance the expected value of discounted future dividends, or as banks controlling their rate of borrowing/lending to a central bank as in the systemic risk model proposed by Carmona et al”
A Probabilistic Approach to Mean Field Games with Major and Minor Players (2014, background): “See for example [9] for some of the striking differences.”
Bellman equation and viscosity solutions for mean-field stochastic control problem (2015, unknown): “2 Inter-bank systemic risk model We consider a model of inter-bank borrowing and lending studied in [15] where the logmonetary reserve of each bank in the asymptotics when the number of banks tend to infinity, is governed by the McKean-Vlasov equation: dXt = [”
Mean Field Control and Mean Field Game Models with Several Populations (2018, background): “Some important applications can be found in finance [47, 4, 42, 18], economy [31, 29, 43, 19, 2, 28], systemic risk [27, 17], energy production [32, 20], or crowd motion [50, 44, 3].”
From the master equation to mean field game limit theory: a central limit theorem (2018, background): “In Section 6 we discuss the linear-quadratic model of [10], which does not fit the assumptions of our main theorems but for which an explicit solution is known for both the n-player and MFG equilibria.”
On the convergence of closed-loop Nash equilibria to the mean field game limit (2018, background): “See [18] for an example of an n-player game in which the unique (and explicit) open-loop and closedloop equilibria are distinct, although they converge to the same limit as n → ∞.”
Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible Resource (2016, background): “[48] and by Lachapelle, Salomon, and Turinici [42]; the influential paper of Lucas and Moll [52]; the work of Carmona, Fouque and Sun on systemic risk [25]; and many other references, many of which can be found in the survey articles [1, 13, 28].”
Superposition and mimicking theorems for conditional McKean–Vlasov equations (2020, background): “1], and also [57, 36, 16, 10, 19, 55, 1, 8, 18, 53, 2, 38, 46]), as well as the dynamics of a particle in the large-scale limit of a particle system with mean field interactions and common noise (see, e.”
Mean field and n‐agent games for optimal investment under relative performance criteria (2017, background): “Beyond the linear quadratic models of Bensoussan, Sung, Yam, and Yung (2016), Carmona, Delarue, and Lachapelle (2013), and Carmona et al. (2015), such examples are scarce, especially in the presence of common noise.”
Deep Fictitious Play for Finding Markovian Nash Equilibrium in Multi-Agent Games (2019, methodology): “For instance, under this framework, Carmona et al. (2015) analyze systemic risk caused by inter-bank lending and borrowing, Achdou et al. (2017) study the income and wealth distribution in macroeconomics, and Bensoussan et al. (2014) model the reinsurance games between insurance companies, just to…”