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In this paper, we study a class of linear-quadratic (LQ) mean-field games in which the individual control process is constrained in a closed convex subset $\Gamma$ of full space $\mathbb{R}^m$. The decentralized strategies and consistency…

Optimization and Control · Mathematics 2016-10-20 Ying Hu , Huang Jianhui , Xun Li

This paper investigates neutral-type McKean-Vlasov stochastic differential equations in which the drift and diffusion coefficients depend on both the segment process and its distribution. Under a one-sided Lipschitz condition on the drift…

Probability · Mathematics 2025-11-25 Zhaohang Wang , Junhao Hu , Chenggui Yuan

This paper focuses on indefinite stochastic mean-field linear-quadratic (MF-LQ, for short) optimal control problems, which allow the weighting matrices for state and control in the cost functional to be indefinite. The solvability of…

Optimization and Control · Mathematics 2020-12-02 Na Li , Xun Li , Zhiyong Yu

The paper is concerned with two-person zero-sum mean-field linear-quadratic stochastic differential games over finite horizons. By a Hilbert space method, a necessary condition and a sufficient condition are derived for the existence of an…

Optimization and Control · Mathematics 2021-06-11 Jingrui Sun , Hanxiao Wang , Zhen Wu

We are interested in the study of stochastic games for which each player faces an optimal stopping problem. In our setting, the players may interact through the criterion to optimise as well as through their dynamics. After briefly…

Probability · Mathematics 2025-09-03 Dylan Possamaï , Mehdi Talbi

We study the discrete-time approximation for solutions of quadratic forward back- ward stochastic differential equations (FBSDEs) driven by a Brownian motion and a jump process which could be dependent. Assuming that the generator has a…

Optimization and Control · Mathematics 2012-11-28 Idris Kharroubi , Thomas Lim

We consider a dynamic traffic routing game over an urban road network involving a large number of drivers in which each driver selecting a particular route is subject to a penalty that is affine in the logarithm of the number of drivers…

Optimization and Control · Mathematics 2020-01-22 Takashi Tanaka , Ehsan Nekouei , Ali Reza Pedram , Karl Henrik Johansson

We develop a model based on mean-field games of competitive firms producing similar goods according to a standard AK model with a depreciation rate of capital generating pollution as a byproduct. Our analysis focuses on the widely-used…

Mathematical Finance · Quantitative Finance 2024-07-18 Gianmarco Del Sarto , Marta Leocata , Giulia Livieri

Mean-field approaches where a complex fermionic many-body problem is replaced by an ensemble of independent particles in a self-consistent mean-field can describe many static and dynamical aspects. It generally provides a rather good…

Nuclear Theory · Physics 2015-06-18 Denis Lacroix , Sakir Ayik

We study an online vector balancing problem, in which $n$ independent Gaussian random vectors $\boldsymbol{\zeta}(1),\dots,\boldsymbol{\zeta}(n) \sim \mathcal{N}(0, I_n)$, each of dimension $n$, arrive one at a time. The goal is to choose…

Probability · Mathematics 2026-05-15 Christian Fiedler , Joe Jackson , Daniel Lacker , Jonathan Niles-Weed

This article examines mean-field-type game problems by means of a direct method. We provide various solvable examples beyond the classical linear-quadratic game problems. These include quadratic-quadratic games and games with power,…

Optimization and Control · Mathematics 2019-04-23 Julian Barreiro-Gomez , Tyrone E. Duncan , Bozenna Pasik-Duncan , Hamidou Tembine

Mean Field Games (MFG) have been introduced to tackle games with a large number of competing players. Considering the limit when the number of players is infinite, Nash equilibria are studied by considering the interaction of a typical…

Optimization and Control · Mathematics 2021-06-14 Mathieu Lauriere

This paper studies a stochastic mean-field linear-quadratic Stackelberg differential game with random coefficients. The interaction between mean-field terms and random coefficients precludes the direct use of conventional decoupling…

Optimization and Control · Mathematics 2026-05-22 Ying Yang , Jie Xiong , Zhouyu Wang

This paper studies multidimensional mean field games with common noise and the related system of McKean-Vlasov forward-backward stochastic differential equations deriving from the stochastic maximum principle. We first propose some…

Probability · Mathematics 2022-12-26 Jodi Dianetti

This paper is concerned with an optimal control problem for a mean-field linear stochastic differential equation with a quadratic functional in the infinite time horizon. Under suitable conditions, including the stabilizability, the…

Optimization and Control · Mathematics 2022-09-26 Jingrui Sun , Jiongmin Yong

We consider a mean-field optimal control problem for stochastic differential equations with delay driven by fractional Brownian motion with Hurst parameter greater than one half. Stochastic optimal control problems driven by fractional…

Optimization and Control · Mathematics 2018-05-02 Nacira Agram , Soukaina Douissi , Astrid Hilbert

We prove the global-in-time well-posedness for a broad class of mean field game problems, which is beyond the special linear-quadratic setting, as long as the mean field sensitivity is not too large. Through the stochastic maximum…

Optimization and Control · Mathematics 2025-01-23 Alain Bensoussan , Ho Man Tai , Tak Kwong Wong , Sheung Chi Phillip Yam

We investigate existence and uniqueness of strong solutions of mean-field stochastic differential equations with irregular drift coefficients. Our direct construction of strong solutions is mainly based on a compactness criterion employing…

Probability · Mathematics 2018-07-02 Martin Bauer , Thilo Meyer-Brandis , Frank Proske

We study a McKean-Vlasov Forward-Backward Stochastic Differential Equation (FBSDE) in connection with the theory of Stochastic Differential Mean-Field games, particularly the weak (non-fully coupled) formulation described in Section 3.3.1…

Optimization and Control · Mathematics 2026-05-08 Hector Sanchez Morgado , Jesus Sierra

In this paper, we present a numerical approach to solve the McKean-Vlasov equations, which are distribution-dependent stochastic differential equations, under some non-globally Lipschitz conditions for both the drift and diffusion…

Numerical Analysis · Mathematics 2023-05-30 Qian Guo , Jie He , Lei Li