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Equilibrium Model of Limit Order Books: A Mean-Field Game View
In this paper, we propose a continuous time equilibrium model of the (sellside) limit order book (LOB) in which the liquidity dynamics follows a...
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The Morse Property of Limit Functions Appearing in Mean Field Equations on Surfaces with Boundary
In this paper, we study the Morse property for functions related to limit functions of mean field equations on a smooth, compact surface
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A singular perturbation problem for mean field games of acceleration: application to mean field games of control
The singular perturbation of mean field game systems arising from minimization problems with control of acceleration is addressed, that is, we...
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Mean Field Markov Decision Processes
We consider mean-field control problems in discrete time with discounted reward, infinite time horizon and compact state and action space. The...
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Swarm gradient dynamics for global optimization: the mean-field limit case
Using jointly geometric and stochastic reformulations of nonconvex problems and exploiting a Monge–Kantorovich (or Wasserstein) gradient system...
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Mean field game of optimal relative investment with jump risk
In this paper, we study the n-player game and the mean field game under the constant relative risk aversion relative performance on terminal wealth,...
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Mean-Field Limits for Entropic Multi-Population Dynamical Systems
The well-posedness of a multi-population dynamical system with an entropy regularization and its convergence to a suitable mean-field approximation...
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Mean-field coupled systems and self-consistent transfer operators: a review
In this review we survey the literature on mean-field coupled maps. We start with the early works from the physics literature, arriving to some...
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Equilibrium States of Mean-Field Models and Bogoliubov’s Approximation Method
Section 5 explains the algebraic approach to quantum statistical mechanics for a large class of...
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General Coupled Mean-Field Reflected Forward-Backward Stochastic Differential Equations
In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations (FBSDEs), whose coefficients not...
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Linear-Quadratic Pareto Cooperative Game for Mean-Field Backward Stochastic System
This paper focuses on a Pareto cooperative differential game with a linear mean-field backward stochastic system and a quadratic form cost...
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A mean field type equation on vector bundles
The mean field type equation is a basic problem of mathematics. Up to now, far too little attention has been paid to the mean field type equation on...
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Sequential Propagation of Chaos for Mean-Field BSDE Systems
A new class of backward particle systems with sequential interaction is proposed to approximate the mean-field backward stochastic differential...
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Incentive Designs for Stackelberg Games with a Large Number of Followers and their Mean-Field Limits
We study incentive designs for a class of stochastic Stackelberg games with one leader and a large number of (finite as well as infinite population...
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Rate of Convergence in the Smoluchowski-Kramers Approximation for Mean-field Stochastic Differential Equations
In this paper we study a second-order mean-field stochastic differential systems describing the movement of a particle under the influence of a...
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Mean field portfolio games
We study mean field portfolio games with random parameters, where each player is concerned with not only her own wealth, but also relative...
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Mean-field optimal control in a multi-agent interaction model for prevention of maritime crime
We study a multi-agent system for the modeling maritime crime. The model involves three interacting populations of ships: commercial ships, pirate...
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An Incentive Algorithm for a Closed Stochastic Network: Data and Mean-Field Analysis
The paper deals with a load-balancing algorithm for a closed stochastic network with two zones with different demands. The algorithm is motivated by...
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Multiple-Population Discrete-Time Mean Field Games with Discounted and Total Payoffs: Approximation of Games with Finite Populations
In the paper we present a model of discrete-time mean-field game with multiple populations of players. Its main result shows that the equilibria...