Related papers: Forward-backward stochastic differential equations…
In this paper, we analyze the mean field backward stochastic differential equations (MFBSDEs) with double mean reflections, whose generator and constraints both depend on the distribution of the solution. When the generator is Lipschitz…
Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard…
This paper is mainly concerned with the solutions to both forward and backward mean-field stochastic partial differential equation and the corresponding optimal control problem for mean-field stochastic partial differential equation. We…
This paper studies infinite horizon linear quadratic (LQ) mean field problems with common noise and regime switching, covering both control and game formulations. To establish a theoretical foundation for the LQ framework, we first analyze…
This paper extends the domination-monotonicity conditions, which guarantee the well-posedness of extended mean-filed forward-backward stochastic differential equations (extended MF-FBSDEs), from the previously studied linear framework to a…
We propose a deep learning approach to compute mean field control problems with individual noises. The problem consists of the Fokker-Planck (FP) equation and the Hamilton-Jacobi-Bellman (HJB) equation. Using the differential of the…
Mathematical mean-field approaches have been used in many fields, not only in Physics and Chemistry, but also recently in Finance, Economics, and Game Theory. In this paper we will study a new special mean-field problem in a purely…
We develop the theory of linear-quadratic (LQ) mean field games (MFGs) in Hilbert spaces with common noise modeled by an infinite-dimensional Wiener process that affects the dynamics of all agents. In the presence of common noise, the…
The purpose of this paper is to provide a detailed probabilistic analysis of the optimal control of nonlinear stochastic dynamical systems of the McKean Vlasov type. Motivated by the recent interest in mean field games, we highlight the…
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 game (MFG) problems with rough common noise, in which the representative state dynamics are governed by a controlled rough stochastic differential equation driven by an idiosyncratic Brownian motion and a deterministic…
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…
We consider a stochastic differential game in the context of forward-backward stochastic differential equations, where one player implements an impulse control while the opponent controls the system continuously. Utilizing the notion of…
We present a novel numerical method for solving McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs) with common noise, combining Picard iterations, elicitability and deep learning. The key innovation involves…
Hu et. al 2018 studied a stochastic optimal control problem for fully coupled forward-backward stochastic control systems with a nonempty control domain. By assuming a weakly coupled condition, they established an approach to obtain the…
This article presents the variant of the approach introduced in the recent work of Bensoussan, Wong, Yam and Yuan [13] to the generic first-order mean field game problem. A major contribution here is the provision of new crucial a priori…
This paper focuses on the long-term behavior of solutions to nonlinear stochastic Fokker-Planck equations driven by common noise, where the drift term has a linear dependence on the measure. These equations, which describe the evolution of…
We study the existence of classical solutions to a broad class of local, first order, forward-backward Extended Mean Field Games systems, that includes standard Mean Field Games, Mean Field Games with congestion, and mean field type control…
This paper studies the convergence of mean field games with finite state space to mean field games with a continuous state space. We examine a space discretization of a diffusive dynamics, which is reminiscent of the Markov chain…
We study optimal control for mean-field forward backward stochastic differential equations with payoff functionals of mean-field type. Sufficient and necessary optimality conditions in terms of a stochastic maximum principle are derived. As…