Contents -- Chapter One: Introduction -- 1.1 Dynamic Economics and Optimization -- 1.2 Methods of Dynamic Optimization -- 1.3 Economic Growth -- 1.4 Theories of Market Equilibrium -- 1.5 Business Cycles -- 1.6 Dynamic Games -- 1.7 Models in Finance -- 1.8 Models of Investment -- 1.9 Numerical Methods for Solving First-Order Conditions in Dynamic Optimization Problems -- Chapter Two: Dynamic Optimization in Discrete Time -- 2.1 The Method of Lagrange Multipliers by an Example -- 2.2 The Method of Dynamic Programming by an Example -- 2.3 Solution of a Standard Dynamic Optimization Problem -- 2.4 Numerical Solution by Linear Approximations of λ and g -- 2.5 Sufficient Conditions for a Globally Optimal Solution -- 2.6 Relations to Known Results on Optimization -- Problems -- Chapter Three: Economic Growth -- 3.1 The Brock-Mirman Growth Model -- 3.2 A Multisector Growth Model -- 3.3 A Growth Model Based on Human Capital and Fertility -- 3.4 Technology and Economic Growth -- 3.5 Research and Development and Economic Growth -- Problems -- Chapter Four: Theories of Market Equilibrium -- 4.1 Asset Prices of an Exchange Economy -- 4.2 Equilibrium in a Pure Currency Economy -- 4.3 A Pure Credit Economy with Linear Utility -- 4.4 Money and Interest in a Cash-In-Advance Economy -- 4.5 A One-Sector Model of General Equilibrium -- 4.6 Equilibrium of a Multisector Model -- 4.7 Equilibrium of a One-Sector Model with Tax Distortion -- Problems -- Chapter Five: Business Cycles -- 5.1 Keynes and the Classics -- 5.2 Dynamic Properties of a Multisector Model with Technology Shocks -- 5.3 Estimating Economic Effects of Political Events in China -- 5.4 Estimating and Testing a Base-Line Real Business Cycle Model -- 5.5 Real Business Cycles and Labor Market Fluctuations -- 5.6 Oligopolistic Pricing and Aggregate Demand -- 5.7 Research on Real Business Cycles -- Problems.

Chapter Six: Dynamic Games -- 6.1 A Formulation of Models of Dynamic Games -- 6.2 Price Determination of Duopolists with No Consumer Switching -- 6.3 A Characterization of Subgame Perfect Equilibrium for Infinitely Repeated Games -- 6.4 A Characterization of Subgame Perfect Equilibrium for Dynamic Games -- 6.5 Credible Government Policy -- 6.6 Credible Taxation to Redistribute Income -- Problems -- Chapter Seven: Models in Finance -- 7.1 Stochastic Differential Equations -- 7.2 Dynamic Programming for a Continuous-Time Model -- 7.3 Solution of a Continuous-Time Optimization Problem by Lagrange Multipliers -- 7.4 An Algebraic Method for Finding the Optimal Control Function -- 7.5 Optimum Consumption and Portfolio Selection Over Time -- 7.6 Capital Asset Pricing with Shifts in Investment Opportunities -- 7.7 The Pricing of Options and Corporate Liabilities -- 7.8 Asset Pricing and Portfolio Selection with Noise in Supply -- 7.9 Asset Pricing and Portfolio Selection with Asymmetric Information -- 7.9a The Kalman Filter in Continuous Time -- Problems -- Chapter Eight: Models of Investment -- 8.1 Investment as Exercising an Irreversible Option to Invest -- 8.2 A Simple Model of Investment with Adjustment Cost -- 8.3 Investment as Gradual Capacity Expansion with Adjustment Cost -- 8.4 Optimal Policy for Replacement Investment -- 8.5 Optimal Policy to Retire Human Capital -- 8.6 Some Other Literature on Investment -- Problems -- Chapter Nine: Numerical Methods for Solving First-Order Conditions in Dynamic Optimization Problems -- 9.1 Introduction -- 9.2 Change of Variables -- 9.3 A Short-Cut to Log-Linearize First-Order Conditions -- 9.4 Solving Matrix Riccati Equations Rapidly -- 9.5 Solving Linear First-Order Conditions by the Method of Undetermined Coefficients -- 9.6 Quadratic Approximation to λ in Discrete Time.

9.7 Quadratic Approximation to λ in Continuous Time -- 9.8 Solving First-Order Conditions by the Galerkin Method -- Problems -- References -- List of Mathematical Statements -- Solutions to Selected Problems -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z.