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...

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. -- Differential games ; Nash equilibria ; Pareto improvements.

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.

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...

n an infinite horizon optimal control problem, the Hamiltonian vanishes at the infinite horizon, when the differential 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...

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...