相关论文: Necessary and sufficient optimality conditions for…

We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of…

We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…

We consider a stochastic control problem, where the control domain is convex and the system is governed by a nonlinear backward stochastic differential equation. With a L1 terminal data, we derive necessary optimality conditions in the form…

Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem…

The main purpose of this paper is to establish the first and second order necessary optimality conditions for stochastic optimal controls using the classical variational analysis approach. The control system is governed by a stochastic…

We consider a control problem where the system is driven by a decoupled as well as a coupled forward-backward stochastic differential equation. We prove the existence of an optimal control in the class of relaxed controls, which are…

We consider optimal control problems for systems governed by mean-field stochastic differential equations, where the control enters both the drift and the diffusion coefficient. We study the relaxed model, in which admissible controls are…

The purpose of this paper is to establish the first and second order necessary conditions for stochastic optimal controls in infinite dimensions. The control system is governed by a stochastic evolution equation, in which both drift and…

This paper investigates the near optimal control for a kind of linear stochastic control systems governed by the forward backward stochastic differential equations, where both the drift and diffusion terms are allowed to depend on controls…

We consider a stochastic control problem which is composed of a controlled stochastic differential equation, and whose associated cost functional is defined through a controlled backward stochastic differential equation. Under appropriate…

In this paper, we establish some second order necessary/sufficient optimality conditions for optimal control problems of stochastic evolution equations in infinite dimensions. The control acts on both the drift and diffusion terms and the…

In this paper we consider non convex control problems of stochastic differential equations driven by relaxed controls. We present existence of optimal controls and then develop necessary conditions of optimality. We cover both continuous…

This paper is the first part of our series work to establish pointwise second-order necessary conditions for stochastic optimal controls. In this part, both drift and diffusion terms may contain the control variable but the control region…

We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then…

In this manuscript, we consider a control system governed by a general ordinary differential equation on a Riemannian manifold, with its endpoints satisfying some inequalities and equalities, and its control constrained to a closed convex…

We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…

A general maximum principle (necessary and sufficient conditions) for an optimal control problem governed by a stochastic differential equation driven by an infinite dimensional martingale is established. The solution of this equation takes…

In this paper, we study two kinds of singular optimal controls (SOCs for short) problems where the systems governed by forward-backward stochastic differential equations (FBSDEs for short), in which the control has two components: the…

The purpose of this paper is to derive some pointwise second-order necessary conditions for stochastic optimal controls in the general case that the control variable enters into both the drift and the diffusion terms. When the control…

We study the singular stochastic optimal control problem with model uncertainty, where the necessary conditions determined by the corresponding maximum principle are trivial. Robust integral form and pointwise second order necessary…