Singular perturbations and optimal control of stochastic systems in infinite dimension: HJB equations and viscosity solutions

Optimal Control of ∞-dimensional Stochastic Systems via Generalized Solutions of Hjb Equations

In this paper, we consider optimal feedback control for stochastc infinite dimensional systems. We present some new results on the solution of associated HJB equations in infinite dimensional Hilbert spaces. In the process, we have also developed some new mathematical tools involving distributions on Hilbert spaces which may have many other interesting applications in other fields. We conclude ...

Stochastic Optimal Control in Infinite Dimensions: Dynamic Programming and HJB Equations

Viscosity Solutions Methods for Singular Perturbations in Deterministic and Stochastic Control

Viscosity solutions methods are used to pass to the limit in some penalization problems for rst order and second order, degenerate parabolic, Hamilton-Jacobi-Bellman equations. This characterizes the limit of the value functions of singularly perturbed optimal control problems for nonlinear deterministic systems and controlled degenerate diiusions, respectively. The results cover also cases whe...

HJB Equations for the Optimal Control of Differential Equations with Delays and State Constraints, I: Regularity of Viscosity Solutions

We study a class of optimal control problems with state constraints, where the state equation is a differential equation with delays. This class includes some problems arising in economics, in particular the so-called models with time to build, see [1, 2, 26]. We embed the problem in a suitable Hilbert space H and consider the associated Hamilton-Jacobi-Bellman (HJB) equation. This kind of infi...

Pathwise Stochastic Control Problems and Stochastic HJB Equations

In this paper we study a class of pathwise stochastic control problems in which the optimality is allowed to depend on the paths of exogenous noise (or information). Such a phenomenon can be illustrated by considering a particular investor who wants to take advantage of certain extra information but in a completely legal manner. We show that such a control problem may not even have a “minimizin...