Maximum principle for mean-field jump–diffusion stochastic delay differential equations and its application to finance

Y Shen, Q Meng, P Shi - Automatica, 2014 - Elsevier
This paper investigates a stochastic optimal control problem with delay and of mean-field
type, where the controlled state process is governed by a mean-field jump–diffusion …

A leader-follower stochastic linear quadratic differential game with time delay

J Xu, J Shi, H Zhang - Science China Information Sciences, 2018 - Springer
In this paper, we are concerned with the leader-follower stochastic differential game of Itô
type with time delay appearing in the leader's control. The open-loop solution is explicitly …

[HTML][HTML] Optimal control of mean-field jump-diffusion systems with delay: A stochastic maximum principle approach

Q Meng, Y Shen - Journal of computational and applied mathematics, 2015 - Elsevier
This paper is concerned with an optimal control problem under mean-field jump-diffusion
systems with delay. Firstly, some existence and uniqueness results are proved for a jump …

Linear–quadratic optimal control for time-delay stochastic system with recursive utility under full and partial information

N Li, G Wang, Z Wu - Automatica, 2020 - Elsevier
This article studies a linear–quadratic (LQ) optimal control problem for time-delay stochastic
system with recursive utility under full and partial information. The system is described by an …

Linear–quadratic mean-field game for stochastic delayed systems

J Huang, N Li - IEEE Transactions on Automatic Control, 2018 - ieeexplore.ieee.org
This paper studies the linear-quadratic mean-field game (MFG) for a class of stochastic
delayed systems. We consider a large-population system, where the dynamics of each …

A general maximum principle for optimal control of stochastic differential delay systems

W Meng, J Shi, T Wang, JF Zhang - SIAM Journal on Control and Optimization, 2025 - SIAM
In this paper, we solve an open problem and obtain a general maximum principle for a
stochastic optimal control problem where the control domain is an arbitrary nonempty set …

Sufficient maximum principle for stochastic optimal control problems with general delays

F Zhang - Journal of Optimization Theory and Applications, 2022 - Springer
This paper is to establish a sufficient maximum principle for one kind of stochastic optimal
control problem with three types of delays: a discrete delay, a moving-average delay and a …

Delayed stochastic linear‐quadratic control problem and related applications

L Chen, Z Wu, Z Yu - Journal of Applied Mathematics, 2012 - Wiley Online Library
We discuss a quadratic criterion optimal control problem for stochastic linear system with
delay in both state and control variables. This problem will lead to a kind of generalized …

Maximum principle for nonzero-sum stochastic differential game with delays

L Chen, Z Yu - IEEE Transactions on Automatic Control, 2014 - ieeexplore.ieee.org
In this technical note, we discuss a nonzero-sum stochastic differential game with delays.
Not only the state variable, but also control variables of players involve delays. This kind of …

Stochastic maximum principle for control systems with time-varying delay

Y Han, Y Li - Systems & Control Letters, 2024 - Elsevier
In this paper, we study the stochastic optimal control problem for control systems with time-
varying delay. The corresponding state equation is a kind of stochastic differential delay …