Related papers: Complex Stochastic Optimal Control Foundation of Q…
Viewing stochastic processes through the lens of occupation measures has proved to be a powerful angle of attack for the theoretical and computational analysis of stochastic optimal control problems. We present a simple modification of the…
This paper studies indefinite stochastic linear-quadratic (LQ) optimal control for jump-diffusion systems with random coefficients. We construct an algebraic inverse flow from the zero-control base system, extract the semimartingale kernel…
In this paper, we consider the problem of controlling a diffusion process pertaining to an opioid epidemic dynamical model with random perturbation so as to prevent it from leaving a given bounded open domain. Here, we assume that the…
The ability to characterise a Hamiltonian with high precision is crucial for the implementation of quantum technologies. In addition to the well-developed approaches utilising optimal probe states and optimal measurements, the method of…
The classical maximum principle for optimal stochastic control states that if a control $\hat{u}$ is optimal, then the corresponding Hamiltonian has a maximum at $u=\hat{u}$. The first proofs for this result assumed that the control did not…
In this paper we prove a necessary condition of the optimal control problem for a class of general mean-field forward-backward stochastic systems with jumps in the case where the diffusion coefficients depend on control, the control set…
This paper proposes a new framework to model control systems in which a dynamic friction occurs. The model consists in a controlled differential inclusion with a discontinuous right hand side, which still preserves existence and uniqueness…
We consider an optimal dividend payout problem for an insurance company whose surplus follows the classical Cram\'er-Lundberg model. The dividend rate is subject to a ratcheting constraint (i.e., it must be nondecreasing over time), and the…
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…
We solve explicitly a two-dimensional singular control problem of finite fuel type for infinite time horizon. The problem stems from the optimal liquidation of an asset position in a financial market with multiplicative and transient price…
In Stochastic Optimal Control (SOC) one minimizes the average cost-to-go, that consists of the cost-of-control (amount of efforts), cost-of-space (where one wants the system to be) and the target cost (where one wants the system to arrive),…
The control of relaxation-type systems of ordinary differential equations is investigated using the Hamilton-Jacobi-Bellman equation. First, we recast the model as a singularly perturbed dynamics which we embed in a family of controlled…
We consider an optimal investment and consumption problem for a Black-Scholes financial market with stochastic coefficients driven by a diffusion process. We assume that an agent makes consumption and investment decisions based on CRRA…
Quantum coherence inherently affects the dynamics and the performances of a quantum machine. Coherent control can, at least in principle, enhance the work extraction and boost the velocity of evolution in an open quantum system. Using…
This paper develops a comparison theorem for viscosity solutions of a new class of Hamilton-Jacobi-Bellman (HJB) equations, which is used to solve the separated problem governed by the K-S equation in the Wasserstein space. A distinctive…
We consider the evolution of a quantum simple harmonic oscillator in a general Gaussian state under simultaneous time-continuous weak position and momentum measurements. We deduce the stochastic evolution equations for position and momentum…
A solution to the optimal problem for determining vector fields which maximize (resp. minimize) the transition probabilities from one location to another for a class of reflecting diffusion processes is obtained in the present paper. The…
The paper concerns the infinite dimensional Hamilton-Jacobi-Bellman equation related to optimal control problem regulated by a transport equation with boundary control. A suitable viscosity solution approach is needed in view of the…
In this paper we present a general framework that allows one to study discretization of certain dynamical systems. This generalizes earlier work on discretization of Lagrangian and Hamiltonian systems on tangent bundles and cotangent…
This paper addresses a continuous-time continuous-space chance-constrained stochastic optimal control (SOC) problem via a Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE). Through Lagrangian relaxation, we convert the…