Lecture 9: Applications of stochastic dynamic programming. The one-sector model of optimal growth.

In this lecture we go over some applications of the theory of stochastic dynamic programming in the framework of the well-known basic neoclassical growth model. After studying the sequential form of the problem, we turn to the Bellman equation. By checking if the necessary conditions hold we show that there is a unique value function

Seminar session 4: Solving a Riccati equation for the optimal linear regulator.

When we have a quadratic one-period return function, solving the problem in the optimal linear regulator framework is an effective option. At the core of the framework, there is a Riccati matrix difference equation, as described in Chapter 5 of Ljungqvist – Sargent’s (2018) Recursive macroeconomic theory. Finding the policy function (which is always linear,

Lecture 8: Stochastic dynamic programming. Part B.

In Part B of Lecture 8 we complete our analysis of the theory of stochastic dynamic programming. First, we examine how to check if the assumptions underlying Theorem 9.12 hold. Demonstration is based on the stochastic version of the basic neoclassical growth model as found on p. 275 of the textbook. Then we have a

Lecture 8: Stochastic dynamic programming. Part A.

In this lecture we start studying how to write and solve stochastic dynamic optimization problems on the basis of what we had already learnt on measure theory, integration, and the theory of Markov processes. Our first and foremost concern is to check the applicability of the results regarding deterministic dynamic programs in order to ensure