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In this paper, we investigate the optimal control problem for systems driven by mixed fractional Brownian motion (including a fractional Brownian motion with Hurst parameter $H>1/2$ and the standard Brownian motion). By using Malliavin…
In this paper, we consider a stochastic recursive optimal control problem under model uncertainty. In this framework, the cost function is described by solutions of a family of backward stochastic differential equations. With the help of…
This article is concerned with stochastic control problems for backward doubly stochastic differential equations of mean-field type, where the coefficient functions depend on the joint distribution of the state process and the control…
We study deterministic nonstationary discrete-time optimal control problems in both finite and infinite horizon. With the aid of Gateaux differentials, we prove a discrete-time maximum principle in analogy with the well-known…
This paper studies a time-changed stochastic control problem, where the underlying stochastic process is a L\'evy noise time-changed by an inverse subordinator. We establish a maximum principle theory for the time-changed stochastic control…
This paper presents three versions of maximum principle for a stochastic optimal control problem of Markov regime-switching forward-backward stochastic differential equations with jumps (FBSDEJs). A general sufficient maximum principle for…
In the present paper we derive, via a backward induction technique, and ad hoc maximum principle for an optimal control problem with multiple random terminal times. Therefore we apply the aforementioned result to the case of a linear…
In this paper, the Pontryagin-type maximum principle for optimal control of quantum stochastic systems in fermion fields is obtained. These systems have gained significant prominence in numerous quantum applications ranging from physical…
We investigate a stochastic optimal control problem where the controlled system is depicted as a stochastic differential delayed equation; however, at the terminal time, the state is constrained in a convex set. We firstly introduce an…
In this paper we study the stochastic control problem of partially observed (multi-dimensional) stochastic system driven by both Brownian motions and fractional Brownian motions. In the absence of the powerful tool of Girsanov…
We develop a necessary stochastic maximum principle for a finite-dimensional stochastic control problem in infinite horizon under a polynomial growth and joint monotonicity assumption on the coefficients. The second assumption generalizes…
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…
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…
In this paper, we study the optimal control problem for steering the state covariance of a discrete-time linear stochastic system over a finite time horizon. First, we establish the existence and uniqueness of the optimal control law for a…
In this paper we consider the maximum principle of optimal control for a stochastic control problem. This problem is governed by a system of fully coupled multi-dimensional forward-backward doubly stochastic differential equation with…
We consider a stochastic transportation problem between two prescribed probability distributions (a source and a target) over processes with general drift dependence and with free end times. First, and in order to establish a dual…
We prove a version of the stochastic maximum principle, in the sense of Pontryagin, for the finite horizon optimal control of a stochastic partial differential equation driven by an infinite dimensional additive noise. In particular we…
We discuss a mathematical framework for analysis of optimal control problems on infinite-dimensional manifolds. Such problems arise in study of optimization for partial differential equations with some symmetry. It is shown that some…
In this paper, we investigate a mean-field singular stochastic optimal control problem for systems governed by mean-field regime-switching singular stochastic differential equations. The state process is assumed to depend on both a regular…
We analyze a novel class of rough stochastic control problems that allows for a convenient approach to solving pathwise stochastic control problems with both non-anticipative and anticipative controls. We first establish the well-posedness…