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...

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...

We solve a multi-period portfolio optimization problem using D-Wave Systems' quantum annealer. We derive a formulation of the problem, discuss several possible integer encoding schemes, and present numerical examples that show high success rates. The formulation incorporates transaction costs...

For large portfolio managers, a sequence of single-period optimal positions is rarely multi-period optimal. In particular, transaction costs can prevent large portfolio managers from monetizing most of their forecasting power. The solution is to compute the trading trajectory that comes...