Related papers: Extended mean field games with terminal constraint…
This paper provides a mathematical study of the well-posedness of master equation on finite state space involving terms modelling common noise. In this setting, the solution of the master equation depends on an additional variable modelling…
The purpose of this paper is to explore the necessary conditions for optimality of mean-field forward-backward delay control systems. A new estimate is proved, which is a powerfultool to deal with the optimal control problems of mean-field…
This paper investigates a robust incentive Stackelberg stochastic differential game problem for a linear-quadratic mean field system, where the model uncertainty appears in the drift term of the leader's state equation. Moreover, both the…
This paper is concerned with extending the notion of monotone solution to the mean field game (MFG) master equation to situations in which the coefficients are displacement monotone, instead of the previously introduced notion in the flat…
This paper studies singular mean field control problems and singular mean field stochastic differential games. Both sufficient and necessary conditions for the optimal controls and for the Nash equilibrium are obtained. Under some…
We consider a class of $N$-player games and mean-field games of singular controls with ergodic performance criterion, providing a benchmark case for irreversible investment games featuring mean-field interaction and strategic…
Mean-field games with common noise provide a powerful framework for modeling the collective behavior of large populations subject to shared randomness, such as systemic risk in finance or environmental shocks in economics. These problems…
In this article, we provide an original systematic global-in-time analysis of mean field type control problems on $\mathbb{R}^n$ with generic cost functionals by the modified approach but not the same, firstly proposed in [7], as the…
We establish existence of nearly-optimal controls, conditions for existence of an optimal control and a saddle-point for respectively a control problem and zero-sum differential game associated with payoff functionals of mean-field type,…
The purpose of this paper is to study the following topics and the relation between them: (i) Optimal singular control of mean-field stochastic differential equations with memory, (ii) reflected advanced mean-field backward stochastic…
This article is concerned with an optimal control problem derived by mean-field forward-backward stochastic differential equation with noisy observation, where the drift coefficients of the state equation and the observation equation are…
Financial markets are often driven by latent factors which traders cannot observe. Here, we address an algorithmic trading problem with collections of heterogeneous agents who aim to perform optimal execution or statistical arbitrage, where…
The theory of Mean Field Game of Controls considers a class of mean field games where the interaction is through the joint distribution of the state and control. It is well known that, for standard mean field games, certain monotonicity…
We a controlled system driven by a coupled forward-backward stochastic differential equation (FBSDE) with a non degenerate diffusion matrix. The cost functional is defined by the solution of the controlled backward stochastic differential…
We consider a class of mean field games in which the agents interact through both their states and controls, and we focus on situations in which a generic agent tries to adjust her speed (control) to an average speed (the average is made in…
In this paper we consider stochastic Fokker-Planck Partial Differential Equations (PDEs), obtained as the mean-field limit of weakly interacting particle systems subjected to both independent (or idiosyncratic) and common Brownian noises.…
We study mean field games for large non--exchangeable populations with moderate local interactions and common noise. The finite--player system is driven by two complementary interaction mechanisms : a graphon--type structure, which encodes…
The main goal of this paper is to study a stochastic game connected to a system of forward backward stochastic differential equations (FBSDEs) involving delay and so-called noisy memory. We derive suffcient and necessary maximum principles…
In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from…
We address the numerical approximation of Mean Field Games with local couplings. For power-like Hamiltonians, we consider both unconstrained and constrained stationary systems with density constraints in order to model hard congestion…