Related papers: Optimal stochastic control problem under model unc…
In this paper, problems of optimal control are considered where in the objective function, in addition to the control cost there is a tracking term that measures the distance to a desired stationary state. The tracking term is given by some…
We study the optimal control of discrete time mean filed dynamical systems under partial observations. We express the global law of the filtered process as a controlled system with its own dynamics. Following a dynamic programming approach,…
We consider a finite-time stochastic drift control problem with the assumption that the control is bounded and the system is controlled until the state process leaves the half-line. Assuming general conditions, it is proved that the…
An optimal control problem driven by an ordinary differential equation under continuous state constraints is considered in this study. From an operational point of view, we introduce a discrete state constraints optimal control problem and…
Time change is a powerful technique for generating noises and providing flexible models. In the framework of time changed Brownian and Poisson random measures we study the existence and uniqueness of a solution to a general mean-field…
Optimal control of heterogeneous mean-field stochastic differential equations with common noise has not been addressed in the literature. In this work, we initiate the study of such models. We formulate the problem within a linear-quadratic…
A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…
In this article, two methods for solving mean-field type optimal control problems are proposed and investigated. The two methods are iterative methods: at each iteration, a Hamilton-Jacobi-Bellman equation is solved, for a terminal…
We consider a long-term optimal investment problem where an investor tries to minimize the probability of falling below a target growth rate. From a mathematical viewpoint, this is a large deviation control problem. This problem will be…
In this paper, we develop a theoretical framework for nonlinear stochastic optimal control problems with optimal stopping by establishing a density-based deterministic representation of the underlying diffusion. For state-independent…
We consider an unregularized optimal control problem subject to the steady-state Navier-Stokes equations. We derive the existence of optimal solutions and prove first- and second-order optimality conditions. To approximate solutions to the…
In this paper we study continuous-time stochastic control problems with both monotone and classical controls motivated by the so-called public good contribution problem. That is the problem of n economic agents aiming to maximize their…
This paper provides necessary conditions of optimality for optimal control problems with time delays in both state and control variables. Different versions of the necessary conditions cover fixed end-time problems and, under additional…
This paper studies a class of continuous-time scalar-state stochastic Linear-Quadratic (LQ) optimal control problem with the linear control constraints. Applying the state separation theorem induced from its special structure, we develop…
In this two-part study we develop a general approach to the design and analysis of exact penalty functions for various optimal control problems, including problems with terminal and state constraints, problems involving differential…
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…
This paper explores continuous-time and state-space optimal stopping problems from a reinforcement learning perspective. We begin by formulating the stopping problem using randomized stopping times, where the decision maker's control is…
This paper aims to establish second order necessary conditions for optimal control in quantum stochastic systems. We employ a variational approach, analogous to methods in classical stochastic control, to analyze systems governed by quantum…
We consider a class of finite-horizon, linear-quadratic stochastic control problems, where the probability distribution governing the noise process is unknown but assumed to belong to an ambiguity set consisting of all distributions whose…
We study the problem of optimal inside control of an SPDE (a stochastic evolution equation) driven by a Brownian motion and a Poisson random measure. Our optimal control problem is new in two ways: (i) The controller has access to inside…