Table of Contents

Cover image

Title page

Copyright

Contributors

Acknowledgments

Introduction to the Series

Introduction for Volume 3 of the Handbook of Computational Economics

Chapter 1. Learning About Learning in Dynamic Economic Models

Abstract

1 Introduction

2 The Framework

3 What We Have Learned

4 What We Hope to Learn

5 Algorithms and Codes

6 A Showcase on Active Learning

7 Learning with Forward Looking Variables

8 Other Applications of Active Learning

9 Summary

References

Chapter 2. On the Numerical Solution of Equilibria in Auction Models with Asymmetries within the Private-Values Paradigm

Abstract

1 Motivation and Introduction

2 Theoretical Model

3 Primer on Relevant Numerical Strategies

4 Previous Research Concerning Numerical Solutions

5 Some Examples

6 Comparisons of Relative Performance and Potential Improvements

7 Summary and Conclusions

Acknowledgments

References

Chapter 3. Analyzing Fiscal Policies in a Heterogeneous-Agent Overlapping-Generations Economy

Abstract

1 Introduction

2 Existing Literature

3 Stylized Model Economy

4 Computational Algorithm

5 Calibration to the US Economy

6 Policy Experiments

7 Concluding Remarks

References

Chapter 4. On Formulating and Solving Portfolio Decision and Asset Pricing Problems

Abstract

1 Introduction

2 Discrete Time Portfolio Decision Making

3 Discrete Time Asset Pricing

4 Continuous Time Portfolio Decision Problem

5 Continuous Time Asset Pricing

6 Conclusion

Acknowledgments

References

Chapter 5. Computational Methods for Derivatives with Early Exercise Features

Abstract

1 General Introduction

2 The Problem Statement—In the Case of Stochastic Volatility and Poisson Jump Dynamics

3 American Call Options Under Jump-Diffusion Processes

4 American Call Options under Jump-Diffusion and Stochastic Volatility Processes

5 Conclusion

References

Chapter 6. Solving and Simulating Models with Heterogeneous Agents and Aggregate Uncertainty

Abstract

1 Introduction

2 Example Economy

3 Algorithms—Overview

4 Models with Nontrivial Market Clearing

5 Approximate Aggregation

6 Simulation with a Continuum of Agents

7 Accuracy

8 Comparison

9 Other Types of Heterogeneity

10 Concluding Comments

Acknowledgments

References

Chapter 7. Numerical Methods for Large-Scale Dynamic Economic Models

Abstract

1 Introduction

2 Literature Review

3 The Chapter at a Glance

4 Nonproduct Approaches to Representing, Approximating, and Interpolating Functions

5 Approximation of Integrals

6 Derivative-Free Optimization Methods

7 Dynamic Programming Methods for High-Dimensional Problems

8 Precomputation Techniques

9 Local (Perturbation) Methods

10 Parallel Computation

11 Numerical Analysis of a High-Dimensional Model

12 Numerical Results for the Multicountry Model

13 Conclusion

Acknowledgments

References

Chapter 8. Advances in Numerical Dynamic Programming and New Applications

Abstract

1 Introduction

2 Theoretical Challenges

3 Numerical Methods for Dynamic Programming

4 Tools from Numerical Analysis

5 Shape-preserving Dynamic Programming

6 Parallelization

7 Dynamic Portfolio Optimization with Transaction Costs

8 Dynamic Stochastic Integration of Climate and Economy

9 Conclusions

Acknowledgments

References

Chapter 9. Analysis of Numerical Errors

Abstract

1 Introduction

2 Dynamic Stochastic Economies

3 Numerical Solution of Simple Markov Equilibria

4 Recursive Methods for Non-optimal Economies

5 Numerical Experiments

6 Concluding Remarks

References

Chapter 10. GPU Computing in Economics

Abstract

1 Introduction

2 Basics of GPGPU Computing

3 A Simple GPGPU Example

4 Example: Value Function Iteration

5 Example: A General Equilibrium Asset Pricing Model with Heterogeneous Beliefs

6 The Road Ahead

7 Conclusion

References

Chapter 11. Computing All Solutions to Polynomial Equations in Economics

Abstract

1 Introduction

2 Gröbner Bases and Polynomial Equations

3 Applying Gröbner Bases to Economic Models

4 All-Solution Homotopy Methods

5 Applying Homotopy Methods

6 Conclusion

Acknowledgments

References

Index