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We study the existence of strong solutions for mean-field forward-backward stochastic differential equations (FBSDEs) with measurable coefficients and their implication on the Nash equilibrium of a multi-population mean-field game. More…

Probability · Mathematics 2025-03-14 Kihun Nam , Yunxi Xu

In this paper we consider a mean field optimal control problem with an aggregation-diffusion constraint, where agents interact through a potential, in the presence of a Gaussian noise term. Our analysis focuses on a PDE system coupling a…

Analysis of PDEs · Mathematics 2019-09-25 Jose A. Carrillo , Edgard A. Pimentel , Vardan K. Voskanyan

Mean-field games (MFGs) study the Nash equilibrium of systems with a continuum of interacting agents, which can be formulated as the fixed-point of optimal control problems. They provide a unified framework for a variety of applications,…

Machine Learning · Statistics 2025-12-02 Jiajia Yu , Junghwan Lee , Yao Xie , Xiuyuan Cheng

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

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…

Optimization and Control · Mathematics 2024-01-18 Charles Bertucci , Alekos Cecchin

Motivated by the trade-off between exploitation and exploration in reinforcement learning, we study a continuous-time entropy-regularized mean variance portfolio selection problem in the presence of jumps. We propose an exploratory SDE for…

Optimization and Control · Mathematics 2025-02-26 Christian Bender , Nguyen Tran Thuan

This paper focuses on multi-agent stochastic differential games for jump-diffusion systems. On one hand, we study the multi-agent game for optimal investment in a jump-diffusion market. We derive constant Nash equilibria and provide…

Optimization and Control · Mathematics 2025-04-08 Liwei Lu , Ruimeng Hu , Xu Yang , Yi Zhu

This paper studies regularity property of the value function for an infinite-horizon discounted cost impulse control problem, where the underlying controlled process is a multidimensional jump diffusion with possibly `infinite-activity'…

Optimization and Control · Mathematics 2009-12-18 Mark H. A. Davis , Xin Guo , Guoliang Wu

We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which a linear path functional of the…

Probability · Mathematics 2013-10-17 Salvatore Federico , Peter Tankov

This paper is concerned with the partial information optimal control problem of mean-field type under partial observation, where the system is given by a controlled mean-field forward-backward stochastic differential equation with…

Optimization and Control · Mathematics 2017-08-21 Qingxin Meng , Qiuhong Shi , Maoning Tang

We study convergence rates of the generalized conditional gradient (GCG) method applied to fully discretized Mean Field Games (MFG) systems. While explicit convergence rates of the GCG method have been established at the continuous PDE…

Numerical Analysis · Mathematics 2026-02-13 Haruka Nakamura , Norikazu Saito

Time change is a powerful technique for generating noises and providing flexible models. In the framework of time changed Brownian and Poisson random measures we study the existence and uniqueness of a solution to a general mean-field…

Probability · Mathematics 2016-08-23 Giulia Di Nunno , Hannes Haferkorn

We present an analytic solution of a differential-difference equation that appears when one solves an optimal stopping time problem with state process following a jump-diffusion process. This equation occurs in the context of real options…

Classical Analysis and ODEs · Mathematics 2019-01-29 Cláudia Nunes , Rita Pimentel , Ana Prior

In this paper, we consider a discrete-time Stackelberg mean field game with a leader and an infinite number of followers. The leader and the followers each observe types privately that evolve as conditionally independent controlled Markov…

Systems and Control · Electrical Eng. & Systems 2022-09-21 Deepanshu Vasal , Randall Berry

We consider a general class of nonzero-sum $N$-player stochastic games with impulse controls, where players control the underlying dynamics with discrete interventions. We adopt a verification approach and provide sufficient conditions for…

Optimization and Control · Mathematics 2020-10-06 Matteo Basei , Haoyang Cao , Xin Guo

The first passage time (FPT) problem is ubiquitous in many applications. In finance, we often have to deal with stochastic processes with jump-diffusion, so that the FTP problem is reducible to a stochastic differential equation with…

Computational Engineering, Finance, and Science · Computer Science 2025-10-20 Di Zhang , Roderick V. N. Melnik

In this paper, we study the $extended$ mean field control problem, which is a class of McKean-Vlasov stochastic control problem where the state dynamics and the reward functions depend upon the joint (conditional) distribution of the…

Probability · Mathematics 2022-04-06 Mao Fabrice Djete

In this paper we obtain results for the existence and uniqueness of solutions to coupled Forward-Backward Stochastic Differential Equations (FBSDEs) with jumps defined on a random environment. This environment corresponds to a…

Probability · Mathematics 2024-01-19 Daniel Hernández-Hernández , Joshué Helí Ricalde-Guerrero

We study methods for solving stochastic control problems of systems of forward-backward mean-field equations with delay, in finite or infinite horizon. Necessary and sufficient maximum principles under partial information are given. The…

Optimization and Control · Mathematics 2016-10-31 Nacira Agram , Elin Engen Rose

We prove existence of solutions for a class of systems of subelliptic PDEs arising from Mean Field Game systems with H\"ormander diffusion. These results are motivated by the feedback synthesis Mean Field Game solutions and the Nash…

Analysis of PDEs · Mathematics 2017-12-05 Federica Dragoni , Ermal Feleqi