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...

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...

I study optimal monetary policy in a simple New Keynesian model with portfolio adjustment costs. Purchases of long-term debt by the central bank (quantitative easing; ‘QE') alter the average portfolio return and hence influence aggregate demand and inflation. The central bank chooses the...

Models in the infinite horizon macro-housing literature often assume that borrowers are constrained exclusively by the loan-to-value (LTV) ratio. Motivated by the Swedish micro-data, I explore an alternative arrangement where borrowers are constrained by the feasibility of repayment, but choose...

Models in the infinite horizon macro-housing literature often assume that borrowers are constrained exclusively by the loan-to-value (LTV) ratio. Motivated by the Swedish micro-data, I explore an alternative arrangement where borrowers are constrained by the feasibility of repayment, but choose...

The rate of time preference is traditionally defined as the marginal rate of substitution between current and future consumption. This definition is not applicable when outcomes are indivisible. Such is the case in all discrete-choice dynamic problems which arise, for example, in modeling...

We consider a non-linear PDE that appears in a number of contexts including a one-way CSA, CVA with risky closeout, option pricing with differential borrowing and lending rates, accounting-consistent valuation, and constrained cash supply. We show that its solution is given as the minimum of...