McKean–Vlasov optimal control: the dynamic programming principle

MF Djete, D Possamaï, X Tan - The Annals of Probability, 2022 - projecteuclid.org
We study the McKean–Vlasov optimal control problem with common noise which allow the
law of the control process to appear in the state dynamics under various formulations: strong …

McKean–Vlasov optimal control: limit theory and equivalence between different formulations

MF Djete, D Possamaï, X Tan - Mathematics of Operations …, 2022 - pubsonline.informs.org
We study a McKean–Vlasov optimal control problem with common noise in order to
establish the corresponding limit theory as well as the equivalence between different …

Stability of McKean–Vlasov stochastic differential equations and applications

K Bahlali, MA Mezerdi, B Mezerdi - Stochastics and Dynamics, 2020 - World Scientific
We consider McKean–Vlasov stochastic differential equations (MVSDEs), which are SDEs
where the drift and diffusion coefficients depend not only on the state of the unknown …

Diffusion control and games

J Wendt - 2023 - db-thueringen.de
In this thesis, we consider stochastic control problems and stochastic differential games in
which controllers or players control the diffusion intensities of their individual state …

The role of correlation in diffusion control ranking games

S Ankirchner, N Kazi-Tani, J Wendt - SIAM Journal on Control and …, 2024 - SIAM
This paper studies two-player stochastic differential games with diffusion control on finite
time horizons. The players' state processes are described in terms of controlled martingale …

Compactification in optimal control of McKean‐Vlasov stochastic differential equations

MA Mezerdi - Optimal Control Applications and Methods, 2021 - Wiley Online Library
We study existence and approximation of optimal controls for systems governed by McKean‐
Vlasov stochastic differential equations. It is well known in simple examples that in the …

Necessary and sufficient conditions in optimal control of mean-field stochastic differential equations with infinite horizon

A Roubi, MA Mezerdi - Random Operators and Stochastic Equations, 2022 - degruyter.com
We consider an infinite horizon optimal control of a system where the dynamics evolve
according to a mean-field stochastic differential equation and the cost functional is also of …

On the maximum principle for relaxed control problems of nonlinear stochastic systems

M Mezerdi, B Mezerdi - Advances in Continuous and Discrete Models, 2024 - Springer
We consider optimal control problems for a system governed by a stochastic differential
equation driven by a d-dimensional Brownian motion where both the drift and the diffusion …

Existence of optimal controls for stochastic Volterra equations

A Cárdenas, S Pulido, R Serrano - arXiv preprint arXiv:2207.05169, 2022 - arxiv.org
We provide sufficient conditions that guarantee the existence of relaxed optimal controls in
the weak formulation of control problems for stochastic Volterra equations (SVEs). Our study …

On optimal control of coupled mean-field forward-backward stochastic equations

B Mansouri, B Mezerdi, K Bahlali - Random Operators and …, 2024 - degruyter.com
We consider a control problem for a mean-field coupled forward-backward stochastic
differential equations, called also McKean–Vlasov equation (MF-FBSDE). For this type of …