Classic optimal control in continuous time with applications in economics

Abstract

This report shows the mathematics behind the solution to continuous time optimization problems. It shows how to specify the Hamiltonian function, how to use the Hamiltonian to obtain the optimal conditions for a typical economic optimal control problem and applies these techniques to several optimal control problems commonly encountered in macroeconomics. An appendix shows how to set up the optimal conditions for the case in which the state and co-state variables are both vectors. A second appendix shows how to approach the control situation for a system of optimal control problems where the co-state variable for the first sub-optimal control problem is the state variable for the second sub-optimal control problem.