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Under a Bayesian framework, we formulate the fully sequential sampling and selection decision in statistical ranking and selection as a stochastic control problem, and derive the associated Bellman equation. Using value function…

Machine Learning · Computer Science 2017-10-10 Yijie Peng , Edwin K. P. Chong , Chun-Hung Chen , Michael C. Fu

This paper is concerned with the open-loop time-consistent solution of time-inconsistent mean-field stochastic linear-quadratic optimal control. Different from standard stochastic linear-quadratic problems, both the system matrices and the…

Optimization and Control · Mathematics 2016-08-19 Yuan-Hua Ni , Ji-Feng Zhang , Miroslav Krstic

We study the optimal stopping problem of McKean-Vlasov diffusions when the criterion is a function of the law of the stopped process. A remarkable new feature in this setting is that the stopping time also impacts the dynamics of the…

Probability · Mathematics 2023-01-18 Mehdi Talbi , Nizar Touzi , Jianfeng Zhang

In this paper, we investigate an optimal control problem for McKean-Vlasov stochastic partial differential equations, in which the coefficients depend on the law of the state process. For systems with nonconvex control sets, we establish a…

Probability · Mathematics 2026-03-09 Liangying Chen , Wilhelm Stannat

We study optimal control problems governed by abstract infinite dimensional stochastic differential equations using the dynamic programming approach. In the first part, we prove Lipschitz continuity, semiconcavity and semiconvexity of the…

Optimization and Control · Mathematics 2025-02-27 Filippo de Feo , Andrzej Święch , Lukas Wessels

We consider the control of McKean-Vlasov dynamics whose coefficients have mean field interactions in the state and control. We show that for a class of linear-convex mean field control problems, the unique optimal open-loop control admits…

Optimization and Control · Mathematics 2021-09-27 Christoph Reisinger , Wolfgang Stockinger , Yufei Zhang

We study the optimal control problem for a weighted mean-field system. A new feature of the control problem is that the coefficients depend on the state process as well as its weighted measure and the control variable. By applying…

Optimization and Control · Mathematics 2022-08-25 Yanyan Tang , Jie Xiong

We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes…

Probability · Mathematics 2017-03-09 Huyên Pham

We provide a new version of the Tikhonov theorem for both two-scale forward systems and also two-scale forward-backward systems of stochastic differential equations, which also covers the McKean-Vlasov case. Differently from what is usually…

Probability · Mathematics 2024-03-26 Matteo Burzoni , Alekos Cecchin , Andrea Cosso

In this paper, we study a stochastic recursive optimal control problem in which the system is governed by a functional forward-backward stochastic differential equation. Under standard assumptions, we establish the dynamic programming…

Probability · Mathematics 2013-01-03 Shaolin Ji , Shuzhen Yang

We consider a stochastic control problem with the assumption that the system is controlled until the state process breaks the fixed barrier. Assuming some general conditions, it is proved that the resulting Hamilton Jacobi Bellman equations…

Optimization and Control · Mathematics 2025-03-24 Dariusz Zawisza

We establish an algebraic rate of convergence in the large number of players limit of the value functions of N-particle stochastic control problems towards the value function of the corresponding McKean-Vlasov problem also known as mean…

Optimization and Control · Mathematics 2023-01-09 Pierre Cardaliaguet , Samuel Daudin , Joe Jackson , Panagiotis Souganidis

In this paper, the stochastic verification theorems for stochastic control problems of reflected forward-backward stochastic differential equations are studied. We carry out the work within the frameworks of classical and viscosity…

Optimization and Control · Mathematics 2023-06-07 Lu Liu , Xinlei Hu , Qingmeng Wei

In this paper, we first establish the dynamic programming principle for stochastic optimal control problems defined on compact Riemannian manifolds without boundary. Subsequently, we derive the associated Hamilton-Jacobi-Bellman (HJB)…

Optimization and Control · Mathematics 2025-07-03 Dingqian Gao , Qi Lü

This article is concerned with an optimal control problem derived by mean-field forward-backward stochastic differential equation with noisy observation, where the drift coefficients of the state equation and the observation equation are…

Optimization and Control · Mathematics 2017-01-09 Guangchen Wang , Hua Xiao , Guojing Xing

In this manuscript we consider a class optimal control problem for stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we…

Optimization and Control · Mathematics 2023-02-20 Filippo de Feo , Salvatore Federico , Andrzej Święch

In this paper we are interested in a new type of {\it mean-field}, non-Markovian stochastic control problems with partial observations. More precisely, we assume that the coefficients of the controlled dynamics depend not only on the paths…

Probability · Mathematics 2017-02-21 Rainer Buckdahn , Juan Li , Jin Ma

We discuss and compare two methods of investigations for the asymptotic regime of stochastic differential games with a finite number of players as the number of players tends to the infinity. These two methods differ in the order in which…

Probability · Mathematics 2012-10-23 Rene Carmona , Francois Delarue , Aime Lachapelle

We provide a dynamic programming principle for stochastic optimal control problems with expectation constraints. A weak formulation, using test functions and a probabilistic relaxation of the constraint, avoids restrictions related to a…

Optimization and Control · Mathematics 2012-12-21 Bruno Bouchard , Marcel Nutz

We study the problem of optimal control for mean-field stochastic partial differential equations (stochastic evolution equations) driven by a Brownian motion and an independent Poisson random measure, in the case of \textit{partial…

Optimization and Control · Mathematics 2017-04-12 Roxana Dumitrescu , Bernt Øksendal , Agnès Sulem