Motivated by empirical observations, we assume that the inventory level of a company follows a mean reverting process. The objective of the management is to keep this inventory level as close as possible to a given target; there is a running cost associated with the difference between the actual inventory level and the target. If inventory deviates too much from the target, management may perfo...

Abstract. We study partial information, possibly non-Markovian, singular stochastic control of Itô–Lévy processes and obtain general maximum principles. The results are used to find connections between singular stochastic control, reflected backward stochastic differential equations, and optimal stopping in the partial information case. As an application we give an explicit solution to a class ...

This paper presents a computationally fesible procedure for the optimal control and stochastic simulation of large nonlinear models with rational expectations under the assumption of certainty equivalence.

We consider a class of stochastic control problems where uncertainty is due to driving noises of general nature as well as to rapidly fluctuating processes affecting the drift. We show that, when the noise ”intensity” is small and the fluctuations become fast, the stochastic problems can be approximated by a deterministic one. We also show that the optimal control of the deterministic problem i...

Abstract. The motivation of this paper is to prove verification theorems for stochastic optimal control of finite dimensional diffusion processes without control in the diffusion term, in the case that the value function is assumed to be continuous in time and once differentiable in the space variable (C) instead of once differentiable in time and twice in space (C), like in the classical resul...

The stochastic optimal control uses the differential equation of Bellman and its solution—the Bellman function. We show how the homonym function in harmonic analysis is (and how it is not) the same stochastic optimal control Bellman function. Then we present several creatures from Bellman’s Zoo: a function that proves the inverse Hölder inequality, as well as several other harmonic analysis Bel...

This paper presents a computationally feasible procedure for the optimal control and stochastic simulation of large nonlinear models with rational expectations under the assumption of certainty equivalence.

Within a general abstract framework, we show that any optimal control problem in standard form can be translated into a stochastic target problem as defined in [17], whenever the underlying filtered probability space admits a suitable martingale representation property. This provides a unified way of treating these two classes of stochastic control problems. As an illustration, we show, within ...

A general model of decentralized stochastic control problem in which multiple controllers share part of their information with each other is investigated. The general model subsumes several models of information sharing in decentralized stochastic control as special cases. Structural results for optimal control strategies for the general model are presented. A dynamic program for finding the op...