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This work concerns the optimal control problem for McKean-Vlasov SDEs. We provide explicit conditions to ensure the existence of optimal Markovian feedback controls. Moreover, based on the flow property of the McKean-Vlasov SDE, the dynamic…

Probability · Mathematics 2023-10-18 Jinghai Shao

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 study stochastic optimal control problems of general fully coupled forward-backward stochastic differential equations (FBSDEs). In Li and Wei [8] the authors studied two cases of diffusion coefficients $\sigma$ of FSDEs, in…

Probability · Mathematics 2012-06-26 Juan Li

We study the stochastic control-stopping problem when the data are of polynomial growth. The approach is based on backward stochastic dierential equations (BSDEs for short). The problem turns into the study of a specic reected BSDE with a…

Optimization and Control · Mathematics 2020-05-15 Brahim Asri , Said Hamadène , Khalid Oufdil

We consider controlled stochastic differential equations (SDEs) with measurable coefficients, a uniformly elliptic diffusion coefficient and an $L_d$-drift. No space-regularity will be assumed for the coefficients. In this framework we…

Analysis of PDEs · Mathematics 2025-09-19 David Criens

We consider a non-Markovian optimal stopping problem on finite horizon. We prove that the value process can be represented by means of a backward stochastic differential equation (BSDE), defined on an enlarged probability space, containing…

Probability · Mathematics 2015-02-20 Marco Fuhrman , Huyên Pham , Federica Zeni

This paper is devoted to the stochastic optimal control problem of infinite-dimensional differential systems allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases studied by…

Optimization and Control · Mathematics 2023-07-19 Jinniao Qiu , Yang Yang

We consider the control of semilinear stochastic partial differential equations (SPDEs) via deterministic controls. In the case of multiplicative noise, existence of optimal controls and necessary conditions for optimality are derived. In…

Optimization and Control · Mathematics 2021-10-28 Wilhelm Stannat , Lukas Wessels

We consider a class of stochastic impulse control problems of general stochastic processes i.e. not necessarily Markovian. Under fairly general conditions we establish existence of an optimal impulse control. We also prove existence of…

Probability · Mathematics 2008-06-18 Boualem Djehiche , Said Hamadene , Ibtissam Hdhiri

Using a recently introduced representation of the second order adjoint state as the solution of a function-valued backward stochastic partial differential equation (SPDE), we calculate the viscosity super- and subdifferential of the value…

Probability · Mathematics 2024-06-27 Wilhelm Stannat , Lukas Wessels

We study optimal stochastic control problems of general coupled systems of forward-backward stochastic differential equations with jumps. By means of the It\^o-Ventzell formula the system is transformed to a controlled backward stochastic…

Optimization and Control · Mathematics 2017-01-12 Bernt Øksendal , Agnès Sulem , Tusheng Zhang

We establish a connection between stochastic optimal control and generative models based on stochastic differential equations (SDEs), such as recently developed diffusion probabilistic models. In particular, we derive a…

Machine Learning · Computer Science 2024-03-27 Julius Berner , Lorenz Richter , Karen Ullrich

We consider a pathwise stochastic optimal control problem and study the associated (not necessarily adapted) Hamilton-Jacobi-Bellman stochastic partial differential equation. We show that the value process is the unique solution of this…

Probability · Mathematics 2023-11-02 Neeraj Bhauryal , Ana Bela Cruzeiro , Carlos Oliveira

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

This paper considers optimal control of dynamical systems which are represented by nonlinear stochastic differential equations. It is well-known that the optimal control policy for this problem can be obtained as a function of a value…

Robotics · Computer Science 2014-05-30 Oktay Arslan , Evangelos Theodorou , Panagiotis Tsiotras

In this article, we present a general methodology for stochastic control problems driven by the Brownian motion filtration including non-Markovian and non-semimartingale state processes controlled by mutually singular measures. The main…

Probability · Mathematics 2024-04-04 Dorival Leão , Alberto Ohashi , Francys Andrews de Souza

In this paper we present a novel sampling-based numerical scheme designed to solve a certain class of stochastic optimal control problems, utilizing forward and backward stochastic differential equations (FBSDEs). By means of a nonlinear…

Systems and Control · Computer Science 2020-06-18 Ioannis Exarchos , Evangelos A. Theodorou

In this paper we make a survey on the so called randomization method, a recent methodology to study stochastic optimization problems. It allows to represent the value function of an optimal control problem by a suitable backward stochastic…

Optimization and Control · Mathematics 2025-06-12 Marco Fuhrman

In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle (SMP) for optimal control of stochastic differential equations (SDEs) of mean-field type, in…

Optimization and Control · Mathematics 2014-04-08 Boualem Djehiche , Hamidou Tembine , Raul Tempone

We solve the optimal control problem of a one-dimensional reflected stochastic differential equation, whose coefficients can be path dependent. The value function of this problem is characterized by a backward stochastic partial…

Probability · Mathematics 2019-01-23 Erhan Bayraktar , Jinniao Qiu