In this paper we outline the Lagrangian constrained optimization method to solve complex problems subject to constraints. Firstly we summarize the Lagrangian constrained optimization routine. Secondly we outline a detailed implementation strategy. Thirdly and finally we provide example and solve...

This article presents an algorithm that extends Ljungqvist and Sargent's (2012) dynamic Stackelberg game to the case of dynamic stochastic general equilibrium models including forcing variables. Its first step is the solution of the discounted augmented linear quadratic regulator as in Hansen...

We examine the linear-quadratic (LQ) approximation of non-linear stochastic dynamic optimization problems in macroeconomics, in particular for monetary policy. We make four main contributions: first, we draw attention to a general Hamiltonian framework for LQ approximation due to Magill (1977)....

This algorithm extends Ljungqvist and Sargent (2012) algorithm of Stackelberg dynamic game to the case of dynamic stochastic general equilibrium models including exogenous forcing variables. It is based Anderson, Hansen, McGrattan, Sargent (1996) discounted augmented linear quadratic regulator....

We construct an optimizing-agent model of a closed economy which is simple enough that we can use it to make exact utility calculations. There is a stabilization problem because there are one-period nominal contracts for wages, or prices, or both and shocks that are unknown at the time when...

Monetary policy reaction functions are compared in a simple optimizing model with one-period nominal stickiness, i.i.d. shocks, and no capital accumulation. The interest rate is the instrument and is either kept constant, "interest rate targeting" for short, or used in targeting one of the...

A consistent framework for optimal liquidity management is presented. This framework optimizes the cost of covering expected cashflow gaps without violating regulatory and business constraints. Anticipated economic value loss, cashflow loss, and adverse market impact are the major drivers of...