Conversion of Certain Stochastic Control Problems into Deterministic Control Problems

Deterministic Approximation for Stochastic Control Problems

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...

Optimality of Deterministic Policies for Certain Stochastic Control Problems with Multiple Criteria and Constraints

For single-criterion stochastic control and sequential decision problems, optimal policies, if they exist, are typically nonrandomized. For problems with multiple criteria and constraints, optimal nonrandomized policies may not exist and, if optimal policies exist, they are typically randomized. In this paper we discuss certain conditions that lead to optimality of nonrandomized policies. In th...

Stochastic control problems with delay

We consider optimal control problems for systems described by stochastic differential equations with delay. We state conditions for certain classes of such systems under which the stochastic control problems become finite-dimensional. These conditions are illustrated with three applications. First, we solve some linear quadratic problems with delay. Then we find the optimal consumption rate in ...

Pathwise Stochastic Control Problems and Stochastic

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...

Conversion of Deterministic Models into Stochastic Models