With non-controllable auto-regressive shocks, the welfare of Ramsey optimal policy is the solution of a single Riccati equation of a linear quadratic regulator. The existing theory by Hansen and Sargent (2007) refers to an additional Sylvester equation but miss another equation for computing the...

We propose a Markov-chain approximation method for discrete-time control problems, showing how to reap the speed gains from continuous-time algorithms in this class of models. Our approach specifies a discrete Markov chain on a grid, taking a first-order approximation of conditional...