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Related papers: Two-Person Zero-Sum Stochastic Linear-Quadratic Di…

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Linear-quadratic optimal control problems are considered for mean-field stochastic differential equations with deterministic coefficients. Time-inconsistency feature of the problems is carefully investigated. Both open-loop and closed-loop…

Optimization and Control · Mathematics 2013-05-07 Jiongmin Yong

This paper investigates closed-loop Nash equilibria for discrete-time linear-quadratic (LQ) stochastic nonzero-sum difference games with random coefficients. Unlike existing works, we consider randomness in both state dynamics and cost…

Optimization and Control · Mathematics 2025-07-23 Qingxin Meng , Yiwei Wu

The paper is concerned with a zero-sum Stackelberg stochastic linear-quadratic (LQ, for short) differential game over finite horizons. Under a fairly weak condition, the Stackelberg equilibrium is explicitly obtained by first solving a…

Optimization and Control · Mathematics 2021-10-05 Jingrui Sun , Hanxiao Wang , Jiaqiang Wen

This paper obtains the maximum principle for both stochastic (global) open-loop and stochastic (global) closed-loop Stackelberg differential games. For the closed-loop case, we use the theory of controlled forward-backward stochastic…

Optimization and Control · Mathematics 2012-10-30 Alain Bensoussan , Shaokuan Chen , Suresh P. Sethi

This paper is concerned with a kind of linear-quadratic (LQ, for short) two-person zero-sum stochastic differential game problems with partial observation. We propose the notions of explicit and implicit feedback laws under partial…

Optimization and Control · Mathematics 2025-10-29 Zhiyong Yu , Wanying Yue

This paper investigates an inhomogeneous non-zero-sum linear-quadratic (LQ, for short) differential game problem whose state process and cost functional are regulated by a Markov chain. Under the $L^2$ stabilizability framework, we first…

Optimization and Control · Mathematics 2024-05-17 Fan Wu , Xun Li , Xin Zhang

This paper studies discrete-time two-person nonzero-sum linear quadratic stochastic games with random coefficients. Using convex variational analysis, we derive necessary and sufficient conditions for the existence of open-loop Nash…

Optimization and Control · Mathematics 2026-04-07 Yongpeng Lin , Qingxin Meng , Maoning Tang

This paper addresses a Stackelberg stochastic linear-quadratic (LQ) differential game under closed-loop information, a problem inherently time-inconsistent. Existing approaches rely on solving two coupled Hamilton-Jacobi-Bellman (HJB)…

Optimization and Control · Mathematics 2026-04-27 Qi Lü , Bowen Ma , Hanxiao Wang

We study the closed-loop solvability of a stochastic linear quadratic optimal control problem for systems governed by stochastic evolution equations. This solvability is established by means of solvability of the corresponding Riccati…

Optimization and Control · Mathematics 2019-01-21 Qi Lü

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

This paper formulates and studies a linear quadratic (LQ for short) game problem governed by linear stochastic Volterra integral equation. Sufficient and necessary condition of the existence of saddle points for this problem are derived. As…

Probability · Mathematics 2010-05-31 Tianxiao Wang , Yufeng Shi

The purpose of this paper is to close the remaining gaps in the understanding of the role that the constrained generalized continuous algebraic Riccati equation plays in singular linear-quadratic (LQ) optimal control. Indeed, in spite of…

Optimization and Control · Mathematics 2014-04-08 Augusto Ferrante , Lorenzo Ntogramatzidis

Recently it has been found that for a stochastic linear-quadratic optimal control problem (LQ problem, for short) in a finite horizon, open-loop solvability is strictly weaker than closed-loop solvability which is equivalent to the regular…

Optimization and Control · Mathematics 2018-06-15 Jingrui Sun , Hanxiao Wang , Jiongmin Yong

In this paper, the open-loop, closed-loop, and weak closed-loop solvability for discrete-time linear-quadratic (LQ) control problem is considered due to the fact that it is always open-loop optimal solvable if the LQ control problem is…

Optimization and Control · Mathematics 2025-02-18 Yue Sun , Xianping Wu , Xun Li

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

In this paper, we consider a partial observed two-person zero-sum stochastic differential game problem where the system is governed by a stochastic differential equation of mean-field type. Under standard assumptions on the coefficients,…

Optimization and Control · Mathematics 2016-11-15 Maoning Tang , Qingxin Meng

This paper investigates the non-zero-sum linear-quadratic stochastic Stackelberg differential games with affine constraints, which depend on both the follower's response and the leader's strategy. With the help of the stochastic Riccati…

Optimization and Control · Mathematics 2024-12-30 Zhun Gou , Nan-Jing Huang , Xian-Jun Long , Jian-Hao Kang

The paper investigates the long-time behavior of zero-sum linear-quadratic stochastic differential games, aiming to demonstrate that, under appropriate conditions, both the saddle strategy and the optimal state process exhibit the…

Optimization and Control · Mathematics 2024-06-05 Jingrui Sun , Jiongmin Yong

An optimal control problem is studied for a linear mean-field stochastic differential equation with a quadratic cost functional. The coefficients and the weighting matrices in the cost functional are all assumed to be deterministic.…

Optimization and Control · Mathematics 2016-02-26 Xun Li , Jingrui Sun , Jiongmin Yong

We consider a class of non-cooperative N-player non-zero-sum stochastic differential games with singular controls, in which each player can affect a linear stochastic differential equation in order to minimize a cost functional which is…

Optimization and Control · Mathematics 2023-04-19 Jodi Dianetti