Piecewise deterministic control problems are problems involving stochastic disturbance of a special type. In certain situations, in an otherwise deterministic control system, it may happen that the state jumps at certain stochastic points of time. Examples are sudden oil finds, or sudden...

This paper yields sufficient conditions for Pareto inoptimality of controls forming Nash equilibria in differential games. In Appendix a result on existence of open loop Nash equilibria is added.

In an in_nite horizon optimal control problem, the Hamiltonian vanishes at the in_nite horizon, when the di_erential equation is autonomous. The integrand in the integral criterion may contain the time explicitly, but it has to satisfy certain integrability conditions. A generalization of...

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...

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...

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...