Mean field game with defaultable agents and systemic risk quantified.
problem Modeling systemic risk in a financial system with defaultable agents.
method Introduced a mean field game with default, provided an explicit solution, and derived an equation for default probability evolution.
result Systemic risk is described by the evolution of default probability.
Transformers approximate mean-field dynamics of indistinguishable particles.
problem Approximating the dynamics of indistinguishable particles in complex systems.
method Using transformers to model the mean-field dynamics of interacting particle systems.
result Theoretical bounds on the distance between true and transformer-obtained mean-field dynamics.
Model connects financial contagion models to mean field analysis.
problem Systemic risk in financial networks.
method Combines Eisenberg-Noe and mean field models.
result Mean field limit derived from finite bank system.
Study connects bank default models using dynamic contagion.
problem Understanding default contagion in heterogeneous interbank systems.
method Proposes a dynamic default contagion model with endogenous early defaults for a finite set of banks, reformulating as a stochastic particle system.
result Existence of clearing systems and continuity of the system response for the mean-field problem.
Mean-field approximations simplify insurance liability calculations.
problem High-dimensional system of equations makes insurance liability calculation infeasible.
method Use mean-field model to replace high-dimensional system with a low-dimensional non-linear system.
result Insurance liability converges to mean-field approximation as cohort size increases.
This work develops a particle system to approximate Fisher-Rao gradient flows in mean-field optimization.
problem Optimizing probability measures in neural network contexts.
method Constructing an interacting particle system approximating Fisher-Rao gradient flows.
result Propagation of chaos for the Fisher-Rao gradient flow in entropic mean-field optimization.
Study shows self-exciting shocks increase systemic risk in interbank networks.
problem Systemic risk in interbank lending networks with self-exciting shocks.
method Mean-field model, weak convergence analysis, measure-valued process, law of large numbers.
result Self-exciting shocks increase systemic risk in interbank networks.
The paper analyzes arbitrage opportunities in a large investor market with common stock noises.
problem Identifying arbitrage opportunities in a market with many competitive investors.
method Stochastic differential games and mean-field systems to study market dynamics and optimal arbitrage.
result Optimal arbitrage is characterized by a solution to a Cauchy PDE involving volatility terms.
Derives mean field game equations from microscopic agent dynamics.
problem Modeling behavior of large interacting agents in games.
method Derives mean field game PDEs from deterministic agent dynamics using Nash equilibria and dynamic programming.
result Derives mean field game limits and scales from agent-based financial market model.
Novel approach to Nash equilibrium in mean-field stochastic games with operator resolvents.
problem Finding Nash equilibrium in mean-field stochastic games with mean-field interaction.
method Proposed a novel approach to derive Nash equilibrium semi-explicitly using operator resolvents and stochastic Fredholm equations.
result Equilibrium of the N-player game converges to mean-field equilibrium, and ε-Nash equilibrium derived as a by-product. Study shows uniform-time chaos propagation in mean field Langevin dynamics.
problem Understanding the convergence of marginal distributions in mean field dynamics.
method Assumed functional convexity of energy, used Lp-convergence and Wasserstein metrics. result Uniform-in-time propagation of chaos proved in both L2-Wasserstein and relative entropy. Kernel methods are studied in a mean field limit for high-dimensional data.
problem Analyzing kernel methods in high-dimensional data with many variables.
method Investigation of kernel methods in the mean field limit of interacting particle systems.
result Rigorous mean field limit of kernels and detailed analysis of the limiting reproducing kernel Hilbert space.
We review recent quantitative results on the approximation of mean field diffusion equations by large systems of interacting particles, obtained by optimal coupling methods. These results concern a larger range of models, more precise senses of convergence and links with the long time behaviour of the systems to be con…
Research explores how interconnected systems synchronize and how to control their behavior.
problem Understanding and controlling the behavior of interconnected dynamical systems.
method Mean field games approach applied to controlled coupled oscillators.
result Developed methods to predict and influence emergent phenomena in interconnected systems.
Extends LIBOR market model to reduce exploding scenarios.
problem Exploding scenarios in market-consistent guarantees valuation.
method Mean-field extension of the LIBOR market model.
result Existence and uniqueness of MF-LMM proved.
Robust Q-learning for mean-field control under Wasserstein uncertainty
problem Mean-field control under Wasserstein uncertainty
method Quantization-and-projection scheme with Wasserstein dual reformulation
result Convergence and finite-time iteration bounds
Study approximates operators on labelled conditional distributions for non-exchangeable systems.
problem Approximating operators on constrained probability measures for non-exchangeable systems.
method Combines cylindrical approximations and DeepONet-type neural architecture for finite-dimensional representations.
result Establishes a universal approximation theorem for continuous operators on Mλ. Study analyzes portfolio liquidation games influenced by self-exciting order flow.
problem Analyzing portfolio liquidation strategies with market order dynamics.
method Mean-field control problem, novel FBSDE system, sufficient maximum principle.
result Existence and uniqueness of open-loop Nash equilibria proved.
New algorithm solves complex mean-field Schrödinger bridge problem.
problem Designing a controller for diffusion processes with nonlocal interaction.
method Generalized Hopf-Cole transform and Sinkhorn-type algorithm.
result Convergence guarantees for the proposed algorithm under mild assumptions.
Algorithm learns interaction kernels for particle systems from data.
problem Understanding and modeling interactions in systems of interacting particles.
method Nonparametric algorithm using least squares with regularization, probabilistic error functional, and reproducing kernel Hilbert space convergence.
result The algorithm converges optimally and accurately learns interaction kernels.
A new algorithm speeds up solving complex spin system problems.
problem Finding the lowest energy state in Ising models, which is hard and important.
method Mean-field Annealing from a Random State (MARS) algorithm, combining SA and MFA.
result MARS solves large Ising spin systems and maximum cut problems efficiently.
New methods learn correlated equilibria in large games without structural assumptions.
problem Learning correlated equilibria in large, anonymous games with exponential player count.
method Developed Mean-Field correlated and coarse-correlated equilibria, and used classical algorithms to learn them efficiently.
result Efficiently learned correlated equilibria in all games without structural assumptions.
Develops a control framework for systemic risk under uncertainty.
problem Systemic risk under model uncertainty.
method Linear-quadratic mean-field control framework with viscosity solutions and verification theorems.
result Explicit feedback controls derived from a coupled Riccati system, preserving analytical tractability.
Framework for robust control in cooperative systems with uncertain common noise.
problem Optimizing collective behavior of agents in the presence of uncertain common noise.
method Proposes a robust mean-field control framework and proves existence of optimal controls.
result Existence of optimal open-loop controls linked to a lifted robust Markov decision problem.
In his lectures at College de France, P.L. Lions introduced the concept of Master equation, see [5] for Mean Field Games. It is introduced in a heuristic fashion, from the system of partial differential equations, associated to a Nash equilibrium for a large, but finite, number of players. The method, also explained in…
Study shows how common noise can trigger or prevent blow-ups in a mean-field system.
problem Exploring blow-ups in a mean-field system with common noise.
method Introduced a model with continuous driving dynamics and common Brownian motion noise.
result Global solutions exist and can be realized through a particle system with common noise, and blow-ups can be triggered or prevented by noise.
Solves specific mean-field game equations with ODEs.
problem Mean-field game equations in economic applications.
method Reduces coupled PDEs to a quadratically nonlinear system of ODEs.
result Shows specific data leads to solvable ODE system.
This work studies clustering in transformer models, proving exponential convergence to a single token state.
problem Understanding the long-term behavior of tokens in transformer models.
method Investigates mean-field transformer models under specific conditions to prove exponential convergence to a single state.
result Transformer models synchronize exponentially fast to a single token state with explicit rates.
Paper studies systemic robustness in financial networks using particle systems.
problem Budget control and default risk in regional financial networks.
method Mean-field particle system approach, McKean-Vlasov equations, asymptotic analysis.
result Systemic robustness measured by the proportion of surviving entities in large particle systems.
Efficiently learns MFC systems with unknown dynamics.
problem Learning in multi-agent systems with non-stationary interactions and combinatorial state/action spaces.
method Model-based reinforcement learning algorithm, M3−UCRL, balancing exploration and exploitation. result First general regret bounds for model-based reinforcement learning of MFC systems.
Improved sampling from mean-field stationary distributions.
problem Sampling from the stationary distribution of mean-field SDEs.
method Decoupling the problem into two aspects: approximation of mean-field SDE and sampling from finite-particle distribution.
result Improved guarantees in various settings, including optimizing neural networks.
LoRA fine-tuning causes forgetting, studied via particle system dynamics.
problem Catastrophic forgetting in LoRA fine-tuning.
method Mean-field self-attention model, partial differential equations, dynamical systems.
result Characterization of phase transitions in forgetting behavior.
Study multiple-population games using McKean-Vlasov equations.
problem Mean field games and control problems with multiple populations.
method Coupled forward-backward SDEs and Pontryagin's principle.
result Existence of mean field equilibria under various cooperation scenarios.
A new method eliminates miscalibration in Gaussian process models for dynamical systems.
problem Miscalibration and overestimation of transition function parameters in Gaussian process models.
method Explicitly models the dependence between state trajectories and Gaussian process posterior, eliminating factorization.
result Better predictive performance and more calibrated estimates of the transition function.
A new method uses Mean Field Games to optimize mixture models of Bernoulli and categorical distributions.
problem Optimizing parameters of finite mixture models of Bernoulli and categorical distributions.
method Mean Field Games theory applied to multi-population systems.
result The Mean Field Games approach provides a method to compute mixture model parameters.
The paper studies Hawkes processes under mean-field limits and criticality conditions.
problem Analyzing nearly unstable Hawkes processes in a mean-field regime.
method Extending the method by Jaisson and Rosenbaum, establishing scaling limits and propagation of chaos.
result Scaling limits of Hawkes processes are stochastic Volterra diffusions of affine type, with three distinct limiting regimes.
Study policy gradient for large-agent mean-field control and game in continuous time.
problem Optimal policy learning for large number of agents in continuous-time mean-field systems.
method Policy gradient method applied to linear-quadratic mean-field control and game models.
result Policy gradient converges to optimal solution at a linear rate for both mean-field control and game.
Study shows how capital constraints can lead to systemic crises in financial systems.
problem Impact of regulatory capital constraints on fire sales and financial stability.
method Mean field game model with banks adjusting holdings via trading strategies under regulatory constraints.
result Capital constraints can lead to simultaneous defaults in a substantial proportion of the banking system.
A framework solves parametric families of MFGs efficiently.
problem Efficiently solving MFG systems with varying initial distributions and terminal costs.
method Operator learning framework for parametric families of MFGs.
result Accurate approximation for cybersecurity and quadratic MFGs.
Extends Langevin dynamics for constrained domains.
problem Optimization of constrained probability measures.
method Mirror mean-field Langevin dynamics (MMFLD).
result Linear convergence guarantees and propagation of chaos results.
Study examines large banks' role in interbank markets using game theory.
problem Understanding systemic risk in interbank markets with large banks.
method Mean-field game framework, convex analysis, Monte Carlo simulations.
result Large banks can positively or negatively impact market stability.
Study on kernel methods in large-scale machine learning problems.
problem Large-scale machine learning with many interacting variables.
method Mean field limit analysis of kernels and their Hilbert spaces.
result Mean field convergence of empirical and infinite-sample solutions.
Review of mean-field methods for neural network inference.
problem Understanding neural network learning from a theoretical perspective.
method Mean-field methods, high-temperature expansions, replica method, message passing algorithms.
result Equivalences and complementarities of mean-field methods.
Improved particle approximation for mean-field neural networks.
problem Particle approximation error for mean-field neural networks.
method Improved particle approximation error by leveraging the problem structure in risk minimization.
result Established an LSI-constant-free particle approximation error concerning the objective gap.
We provide bounds on control learning error in stochastic systems.
problem Learning optimal controls in stochastic environments with uncontrolled parts.
method Dynamic programming and mean-field interpretation of neural networks.
result Non-asymptotic bounds on generalization error for stable overparametrised settings.
Modeling systemic risk with contagion effects in financial systems.
problem Capturing systemic risk and contagion effects in large financial systems.
method Dynamic mean field model derived from interacting diffusions with an absorbing boundary.
result The SPDE model exhibits periods of significant default clustering due to contagion.
Improved disability insurance model with collective health claims.
problem Enhance disability insurance model with collective health claims.
method Expand classic semi-Markov model with collective health claims, solve many-body problem using mean-field approach.
result Mean-field approach simplifies complex model into a transparent pricing method.
Conservative SPDEs emerge from fluctuating SGD dynamics in neural networks.
problem Understanding the convergence of stochastic gradient descent to SPDEs.
method Mean-field analysis and central limit theorem for SPDEs.
result Optimal convergence rates for SPDEs derived from SGD.