Excerpt from lecture notes:

The objective of this course is to provide a toolbox for solving maximization problems and for working with their solutions in economic models. Maximization problems can be formulated in discrete or continuous time, under certainty or uncertainty. Various maximization methods will be used, ranging from “solving by inserting”, via La- grangian and Hamiltonian approaches to dynamic programming (Bellman equation). Dynamic programming will be used for all environments, discrete, continuous, certain and uncertain, the Lagrangian for most of them. Solving by inserting is also very useful in discrete time setups. The Hamiltonian approach is used only for deterministic continuous time setups. An overview is given on the next page.

Part I deals with discrete time models under certainty, Part II covers continuous time models under certainty. Part III deals with discrete time models under uncertainty and Part IV, logically, analyzes continuous time models under uncertainty.

The course is called “applied intertemporal optimization“, where the emphasis is on “applied”. This means that each type of maximization problem will be illustrated by some example from the literature. These will come from micro- and macroeconomics, from finance, environmental economics and game theory. This also means, maybe more importantly, that there is little emphasis on formal scrutiny. This course is about computing solutions. A more formal treatment (especially of the stochastic part) can be found elsewhere in the literature and many references will be given.