By means of some simple examples from economics, we elucidatecertain solution tools for the solution of optimal control problems were the system under study undergoes major changes when certain boundaries are crossed. The "major changes" may be that the state gets a jump discontinuity when...

Frequently controls forming Nash equilibria in differential games are not Pareto optimal. This paper presents conditions that can be used to show the existence of strict Pareto improvements of Nash equilibria in such games. The conditions are based on standard tools in control theory. Copyright...

A maximum principle is proved for certain problems of continuous time stochastic control with hard end constraints, (end constraints satis_ed a.s.) After establishing a general theorem, the results are applied to problems where the state equation (di_erential equation) changes at certain...

Open mapping theorems are proved for directionally differentiable Lipschitz continuous functions. It is indicated that generalizations to nonsmooth functions that are not directionally differentiable are possible. The results in the paper generalize the open mapping theorems for differentiable...

Abstract Optimal nonanticipating controls are shown to exist in nonautonomous piecewise deterministic control problems with hard terminal restrictions. The assumptions needed are completely analogous to those needed to obtain optimal controls in deterministic control problems. The proof is based...