Related papers: Dynamic Programming Principle for Stochastic Contr…
In this paper we study an optimization problem in which the control is information, more precisely, the control is a $\sigma$-algebra or a filtration. In a dynamic setting, we establish the dynamic programming principle and the law…
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…
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 work, we consider the local Cahn-Hilliard-Navier-Stokes equation with regular potential in two dimensional bounded domain. We formulate distributed optimal control problem as the minimization of a suitable cost functional subject to…
We consider a stochastic optimal control problem where the controller can anticipate the evolution of the driving noise over some dynamically changing time window. The controlled state dynamics are understood as a rough differential…
A large number of recent studies consider a compartmental SIR model to study optimal control policies aimed at containing the diffusion of COVID-19 while minimizing the economic costs of preventive measures. Such problems are non-convex and…
In this paper, we study an optimal stopping problem in the presence of model uncertainty and regime switching. The max-min formulation for robust control and the dynamic programming approach are adopted to establish a general theoretical…
We study the optimal control of path-dependent piecewise deterministic processes. An appropriate dynamic programming principle is established. We prove that the associated value function is the unique minimax solution of the corresponding…
The aim of this work is to develop a deep learning method for solving high-dimensional stochastic control problems based on the Hamilton--Jacobi--Bellman (HJB) equation and physics-informed learning. Our approach is to parameterize the…
This paper studies an optimal stochastic impulse control problem in a finite horizon with a decision lag, by which we mean that after an impulse is made, a fixed number units of time has to be elapsed before the next impulse is allowed to…
In optimal control problems defined on stratified domains, the dynamics and the running cost may have discontinuities on a finite union of submanifolds of RN. In [8, 5], the corresponding value function is characterized as the unique…
This paper studies an optimal dividend problem with a drawdown constraint in a Brownian motion model, requiring the dividend payout rate to remain above a fixed proportion of its historical maximum. This leads to a path-dependent stochastic…
We study a specific class of finite-horizon mean field optimal stopping problems by means of the dynamic programming approach. In particular, we consider problems where the state process is not affected by the stopping time. Such problems…
We consider an infinite horizon control problem for dynamics constrained to remain on a multidimensional junction with entry costs. We derive the associated system of Hamilton-Jacobi equations (HJ), prove the comparison principle and that…
Recent studies have extended the use of the stochastic Hamilton-Jacobi-Bellman (HJB) equation to include complex variables for deriving quantum mechanical equations. However, these studies often assume that it is valid to apply the HJB…
In this article, the notion of viscosity solution is introduced for the path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with the optimal control problems for path-dependent stochastic differential equations. We identify…
We develop dynamical programming methods for the purpose of optimal control of quantum states with convex constraints and concave cost and bequest functions of the quantum state. We consider both open loop and feedback control schemes,…
We characterize the value of swing contracts in continuous time as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation with suitable boundary conditions. The case of contracts with penalties is straightforward, and in that…
We consider a singular control problem with regime switching that arises in problems of optimal investment decisions of cash-constrained firms. The value function is proved to be the unique viscosity solution of the associated…
We study the Hamilton-Jacobi equation for undiscounted exit time control problems with general nonnegative Lagrangians using the dynamic programming approach. We prove theorems characterizing the value function as the unique…