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This paper is concerned with a stochastic linear-quadratic optimal control problem in a finite time horizon, where the coefficients of the control system are allowed to be random, and the weighting matrices in the cost functional are…

Optimization and Control · Mathematics 2019-11-12 Jingrui Sun , Jie Xiong , Jiongmin Yong

The objective of the present paper is to investigate the solution of fully coupled mean-field forward-backward stochastic differential equations (FBSDEs in short) and to study the stochastic control problems of mean-field type as well as…

Optimization and Control · Mathematics 2012-07-19 Ruimin Xu , Liangquan Zhang

The theory of mean field games is a tool to understand noncooperative dynamic stochastic games with a large number of players. Much of the theory has evolved under conditions ensuring uniqueness of the mean field game Nash equilibrium.…

Optimization and Control · Mathematics 2019-03-19 Bruce Hajek , Michael Livesay

We propose a new approach to mean field games with major and minor players. Our formulation involves a two player game where the optimization of the representative minor player is standard while the major player faces an optimization over…

Probability · Mathematics 2014-09-26 Rene Carmona , Xiuneng Zhu

This paper investigates a conditional mean-field type linear quadratic (LQ) optimal control problem with partial observation and regime switching, where the conditional expectations of the state and control given the history of Markov chain…

Optimization and Control · Mathematics 2025-12-22 Zhongbin Guo , Guangchen Wang

In this work, we study a class of stationary mean-field games of singular stochastic control under model uncertainty. The representative agent adjusts the dynamics of an It\^o diffusion via one-sided singular stochastic control, aiming to…

Optimization and Control · Mathematics 2025-05-14 Giorgio Ferrari , Ioannis Tzouanas

In this paper, we concern with the ergodic linear-quadratic closed-loop optimal control problems with random periodic coefficients. We put forward the random periodic mean-square exponentially stable condition, and prove the random…

Optimization and Control · Mathematics 2026-01-14 Jiacheng Wu , Qi Zhang

We study discrete-time mean-field Markov games with infinite numbers of agents where each agent aims to minimize its ergodic cost. We consider the setting where the agents have identical linear state transitions and quadratic cost…

Optimization and Control · Mathematics 2019-10-17 Zuyue Fu , Zhuoran Yang , Yongxin Chen , Zhaoran Wang

The classical stochastic control problem under partial information can be formulated as a control problem for Zakai equation, whose solution is the unnormalized conditional probability distribution of the state of the system. Zakai equation…

Optimization and Control · Mathematics 2019-09-27 Alain Bensoussan , Sheung Chi Phillip Yam

This paper studies an asymptotic solvability problem for linear quadratic (LQ) mean field games with controlled diffusions and indefinite weights for the state and control in the costs. We employ a rescaling approach to derive a low…

Optimization and Control · Mathematics 2021-09-20 Minyi Huang , Xuwei Yang

In this paper, we study a class of real-valued mean-field backward stochastic differential equations (BSDEs) with generators of quadratic growth in the control variable and the mean-field term. Under this assumption, together with a bounded…

Optimization and Control · Mathematics 2026-02-17 Yining Ding , Kihun Nam , Jiaqiang Wen

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

An optimal ergodic control problem (EC problem, for short) is investigated for a linear stochastic differential equation with quadratic cost functional. Constant nonhomogeneous terms, not all zero, appear in the state equation, which lead…

Optimization and Control · Mathematics 2020-04-24 Hongwei Mei , Qingmeng Wei , Jiongmin Yong

This paper studies relative arbitrage opportunities in a market with competitive investors through stochastic differential games in the limit as the number of players tends to infinity. With common noises introduced by the stock…

Mathematical Finance · Quantitative Finance 2025-11-24 Nicole Tianjiao Yang , Tomoyuki Ichiba

We investigate the convergence of symmetric stochastic differential games with interactions via control, where the volatility terms of both idiosyncratic and common noises are controlled. We apply the stochastic maximum principle, following…

Probability · Mathematics 2026-02-19 Erhan Bayraktar , Hiroaki Horikawa

In this paper, we investigate a class of time-inconsistent discrete-time stochastic linear-quadratic optimal control problems, whose time-consistent solutions consist of an open-loop equilibrium control and a linear feedback equilibrium…

Optimization and Control · Mathematics 2017-03-07 Xun Li , Yuan-Hua Ni , Ji-Feng Zhang

Motivated by the recent applications of game-theoretical learning techniques to the design of distributed control systems, we study a class of control problems that can be formulated as potential games with continuous action sets, and we…

Optimization and Control · Mathematics 2014-12-03 Steven Perkins , Panayotis Mertikopoulos , David S. Leslie

This paper studies social optima and Nash games for mean field linear quadratic control systems, where subsystems are coupled via dynamics and individual costs. For the social control problem, we first obtain a set of forward-backward…

Optimization and Control · Mathematics 2019-04-17 Bingchang Wang , Huanshui Zhang

We study the asymptotic behavior of solutions to linear-quadratic mean field stochastic optimal control problems. By formulating an ergodic control framework, we characterize the convergence between the finite time horizon control problem…

Optimization and Control · Mathematics 2025-10-24 Erhan Bayraktar , Jiamin Jian

This paper is concerned with a mean-field linear quadratic (LQ, for short) optimal control problem with deterministic coefficients. It is shown that convexity of the cost functional is necessary for the finiteness of the mean-field LQ…

Optimization and Control · Mathematics 2015-09-16 Jingrui Sun