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In this paper, we study a stochastic optimal control problem under degenerate G-expectation. By using implied partition method, we show that the approximation result for admissible controls still hold. Based on this result, we prove that…

Optimization and Control · Mathematics 2022-10-19 Xiaojuan Li

We consider a kind of stochastic exit time optimal control problems, in which the cost function is defined through a nonlinear backward stochastic differential equation. We study the regularity of the value function for such a control…

Probability · Mathematics 2016-03-15 Rainer Buckdahn , Tianyang Nie

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 a stochastic recursive optimal control problem in which the objective functional is described by the solution of a backward stochastic differential equation driven by G-Brownian motion. Under standard assumptions, we…

Optimization and Control · Mathematics 2013-06-07 Mingshang Hu , Shaolin Ji , Shuzhen Yang

In this paper we investigate a kind of optimal control problem of coupled forward-backward stochastic system with jumps whose cost functional is defined through a coupled forward-backward stochastic differential equation with Brownian…

Probability · Mathematics 2020-09-15 Qian Lin

In this paper, we study the optimal singular controls for stochastic recursive systems, in which the control has two components: the regular control, and the singular control. Under certain assumptions, we establish the dynamic programming…

Optimization and Control · Mathematics 2018-11-06 Liangquan Zhang

We consider a robust switching control problem. The controller only observes the evolution of the state process, and thus uses feedback (closed-loop) switching strategies, a non standard class of switching controls introduced in this paper.…

Probability · Mathematics 2016-07-04 Erhan Bayraktar , Andrea Cosso , Huyen Pham

We study the properties of the value function associated with an optimal control problem with uncertainties, known as average or Riemann-Stieltjes problem. Uncertainties are assumed to belong to a compact metric probability space, and…

Optimization and Control · Mathematics 2024-07-19 M. Soledad Aronna , Michele Palladino , Oscar Sierra

In this paper, we study a stochastic recursive optimal control problem in which the cost functional is described by the solution of a backward stochastic differential equation driven by G-Brownian motion. Under standard assumptions, we…

Optimization and Control · Mathematics 2014-10-15 Mingshang Hu , Shaolin Ji

We analyze an optimal stopping problem with a constraint on the expected cost. When the reward function and cost function are Lipschitz continuous in state variable, we show that the value of such an optimal stopping problem is a continuous…

Optimization and Control · Mathematics 2017-08-08 Erhan Bayraktar , Song Yao

We apply the stochastic Perron method of Bayraktar and S\^irbu to a general infinite horizon optimal control problem, where the state $X$ is a controlled diffusion process, and the state constraint is described by a closed set. We prove…

Optimization and Control · Mathematics 2014-09-25 Dmitry B. Rokhlin

In this paper, we propose and study the stochastic path-dependent Hamilton-Jacobi-Bellman (SPHJB) equation that arises naturally from the optimal stochastic control problem of stochastic differential equations with path-dependence and…

Probability · Mathematics 2020-06-24 Jinniao Qiu

This paper is devoted to the stochastic optimal control problem of ordinary differential equations allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases, the value function turns…

Optimization and Control · Mathematics 2021-10-25 Jinniao Qiu

This paper is concerned with stochastic impulse control problems in which the running cost changes depending on the impulse control. Because of such a dependence, it brings several difficulties when the usual dynamic programming principle…

Optimization and Control · Mathematics 2025-11-11 Yuchen Cao , Jiongmin Yong

In this paper, we study the delayed stochastic recursive optimal control problem with a non-Lipschitz generator, in which both the dynamics of the control system and the recursive cost functional depend on the past path segment of the state…

Optimization and Control · Mathematics 2023-12-27 Jiaqiang Wen , Zhen Wu , Qi Zhang

In this paper, we study backward doubly stochastic recursive optimal control problem where the cost function is described by the solution of a backward doubly stochastic differential equation. We give the dynamical programming principle for…

Probability · Mathematics 2020-08-13 Yunhong Li , Anis. Matoussi , Lifeng Wei , Zhen Wu

In this manuscript, we study optimal control problems for stochastic delay differential equations using the dynamic programming approach in Hilbert spaces via viscosity solutions of the associated Hamilton-Jacobi-Bellman equations. We show…

Optimization and Control · Mathematics 2024-12-24 Filippo de Feo , Andrzej Święch

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 a stochastic optimal control problem governed by a stochastic differential equation with delay in the control. Using a result of existence and uniqueness of a sufficiently regular mild solution of the associated…

Probability · Mathematics 2021-03-22 F. Gozzi , F. Masiero

We introduce a probabilistic version of the classical Perron's method to construct viscosity solutions to linear parabolic equations associated to stochastic differential equations. Using this method, we construct easily two viscosity (sub…

Probability · Mathematics 2011-07-14 Erhan Bayraktar , Mihai Sirbu