LQ Control¶

Lectures¶

• Information and Consumption Smoothing
  • Overview
  • Two Representations of the Same Nonfinancial Income Process
  • State Space Representations
• Consumption Smoothing with Complete and Incomplete Markets
  • Overview
  • Background
  • Linear State Space Version of Complete Markets Model
  • Model 1 (Complete Markets)
  • Model 2 (One-Period Risk-Free Debt Only)
• Tax Smoothing with Complete and Incomplete Markets
  • Overview
  • Tax Smoothing with Complete Markets
  • Returns on State-Contingent Debt
  • More Finite Markov Chain Tax-Smoothing Examples
• Robustness
  • Overview
  • The Model
  • Constructing More Robust Policies
  • Robustness as Outcome of a Two-Person Zero-Sum Game
  • The Stochastic Case
  • Implementation
  • Application
  • Appendix
• Markov Jump Linear Quadratic Dynamic Programming
  • Overview
  • Review of useful LQ dynamic programming formulas
  • Linked Ricatti equations for Markov LQ dynamic programming
  • Applications
  • Example 1
  • Example 2
  • More examples
• How to Pay for a War: Part 1
  • Reader’s Guide
  • Public Finance Questions
  • Barro (1979) Model
  • Python Class to Solve Markov Jump Linear Quadratic Control Problems
  • Barro Model with a Time-varying Interest Rate
• How to Pay for a War: Part 2
  • An Application of Markov Jump Linear Quadratic Dynamic Programming
  • Two example specifications
  • One- and Two-period Bonds but No Restructuring
  • Mapping into an LQ Markov Jump Problem
  • Penalty on Different Issuance Across Maturities
  • A Model with Restructuring
  • Restructuring as a Markov Jump Linear Quadratic Control Problem
• How to Pay for a War: Part 3
  • Another Application of Markov Jump Linear Quadratic Dynamic Programming
  • Roll-Over Risk
  • A Dead End
  • Better Representation of Roll-Over Risk
• Optimal Taxation in an LQ Economy
  • Overview
  • The Ramsey Problem
  • Implementation
  • Examples
  • Exercises
  • Solutions