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, thanks to the quadratic one-period return function) takes solving the value function, and the matrix 'in the middle' of the value function is the fixed point of the Riccati equation. The idea behind solving this Riccati equation is thus straightforward: We only need to find the fixed point in an iterative process. This Matlab session builds upon this idea by establishing an iterative algorithm on the basis of a series of matrices, where the stopping criterion given as on order to break the 'for loop' is defined by the difference of consecutive matrices that falls under a chosen threshold.

Title page:(00:00)
Ljungqvist – Sargent (2018): Exercise 7.1:(00:10)
MATLAB session:(01:59)