Efficient Implementation of the Riccati Recursion for Solving Linear-Quadratic Control Problems

in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is typically the main computational effort at each iteration. In this paper, we compare a number of solvers for an extended formulation of the LQ control problem: a Riccati recursion based solver can be considered the best choice for the general problem with dense matrices. Furthermore, we present a novel version of the Riccati solver, that makes use of the Cholesky factorization of the Pn matrices to reduce the number of flops. When combined with regularization and mixed precision, this algorithm can solve large instances of the LQ control problem up to 3 times faster than the classical Riccati solver. I

Exotic Preferences for Macroeconomists

We provide a user's guide to exotic' preferences: nonlinear time aggregators, departures from expected utility, preferences over time with known and unknown probabilities, risk-sensitive and robust control, hyperbolic' discounting, and preferences over sets ( temptations'). We apply each to a number of classic problems in macroeconomics and finance, including consumption and saving, portfolio choice, asset pricing, and Pareto optimal allocations.