Related papers: Optimal control on graphs: existence, uniqueness, …
We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…
A general method to describe stochastic dynamics of Markov processes is suggested. The method aims to solve three related problems. The determination of an optimal coordinate for the description of stochastic dynamics. The reconstruction of…
This paper is concerned with the existence of optimal controls for backward stochastic partial differential equations with random coefficients, in which the control systems are represented in an abstract evolution form, i.e. backward…
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…
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…
We characterize the optimal control for a class of singular stochastic control problems as the unique solution to a related Skorokhod reflection problem. The considered optimization problems concern the minimization of a discounted cost…
We show a connection between global unconstrained optimization of a continuous function $f$ and weak KAM theory for an eikonal-type equation arising also in ergodic control. A solution $v$ of the critical Hamilton-Jacobi equation is built…
In this paper we present a dynamic programing approach to stochastic optimal control problems with dynamic, time-consistent risk constraints. Constrained stochastic optimal control problems, which naturally arise when one has to consider…
In this paper we study the existence of sufficiently regular representations of Hamilton-Jacobi equations in the optimal control theory with unbounded control set. We use a new method to construct representations for a wide class of…
We study a multiscale stochastic optimal control problem subject to state constraints on the slow variable. To address this class of problems, we develop a rigorous theoretical framework based on singular perturbation analysis, tailored to…
This paper examines stochastic optimal control problems in which the state is perfectly known, but the controller's measure of time is a stochastic process derived from a strictly increasing L\'evy process. We provide dynamic programming…
We study the asymptotic behavior of solutions to linear-quadratic mean field stochastic optimal control problems. By formulating an ergodic control framework, we characterize the convergence between the finite time horizon control problem…
In this article we study a finite horizon optimal control problem with monotone controls. We consider the associated Hamilton-Jacobi-Bellman (HJB) equation which characterizes the value function. We consider the totally discretized problem…
Stochastic optimal control problems for Hamiltonian dynamics on graphs have wide-ranging applications in mechanics and quantum field theory, particularly in systems with graph-based structures. In this paper, we establish the existence and…
In this paper, we investigate dynamic optimization problems featuring both stochastic control and optimal stopping in a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed…
In this paper, we propose a unified stochastic optimal control framework that integrates time-optimal control problems with classical stochastic optimal control formulations. Unlike conventional deterministic time-optimal control models,…
In this paper, we concern with the ergodic linear-quadratic closed-loop optimal control problems, in which the state equation is the mean-field stochastic differential equation with periodic coefficients. We first study the asymptotic…
In this note, we study a class of indefinite stochastic McKean-Vlasov linear-quadratic (LQ in short) control problem under the control taking nonnegative values. In contrast to the conventional issue, both the classical dynamic programming…
This paper is concerned with a partially observed hybrid optimal control problem, where continuous dynamics and discrete events coexist and in particular, the continuous dynamics can be observed while the discrete events, described by a…
In this paper we introduce a new kind of Backward Stochastic Differential Equations, called ergodic BSDEs, which arise naturally in the study of optimal ergodic control. We study the existence, uniqueness and regularity of solution to…