Applied Computational Economics and Finance

Size: px

Start display at page:

Download "Applied Computational Economics and Finance"

Olivia Williams
8 years ago
Views:

1 Applied Computational Economics and Finance Mario J. Miranda and Paul L. Fackler The MIT Press Cambridge, Massachusetts London, England

2 Preface xv 1 Introduction Some Apparently Simple Questions An Alternative Analytic Framework 3 Exercises 4 2 Linear Equations and Computer Basics L-U Factorization Gaussian Elimination Rounding Error Ill Conditioning Special Linear Equations Iterative Methods 16 Exercises 19 Appendix 2A: Computer Arithmetic 20 Appendix 2B: Data Storage 24 Bibliographie Notes 26 3 Nonlinear Equations and Complementarity Problems Bisection Method Function Iteration Newton's Method Quasi-Newton Methods Problems with Newton Methods Choosing a Solution Method Complementarity Problems Complementarity Methods 47 Exercises 52 Bibliographie Notes 57 4 Finite-Dimensional Optimization Derivative-Free Methods Newton-Raphson Method Quasi-Newton Methods Line Search Methods 70

6 Iterative Methods 16 Exercises 19 Appendix 2A: Computer Arithmetic 20 Appendix 2B: Data Storage 24 Bibliographie Notes 26 3 Nonlinear Equations and Complementarity Problems 29 3.

3 viii Contents 4.5 Special Cases Constrained Optimization 74 Exercises 78 Bibliographie Notes 83 5 Numerical Integration and Differentiation Newton-Cotes Methods Gaussian Quadrature Monte Carlo Integration Quasi-Monte Carlo Integration An Integration Tool Kit Numerical Differentiation Initial Value Problems 105 Exercises 110 Bibliographie Notes Function Approximation Interpolation Principles Polynomial Interpolation Piecewise Polynomial Splines Piecewise Linear Basis Functions Multidimensional Interpolation Choosing an Approximation Method An Approximation Tool Kit The Collocation Method Boundary Value Problems 146 Exercises 149 Bibliographie Notes Discrete Time, Discrete State Dynamic Models Discrete Dynamic Programming Economic Examples Mine Management Asset Replacement Asset Replacement with Maintenance 159

7 Initial Value Problems 105 Exercises 110 Bibliographie Notes 114 6 Function Approximation 115 6.1 Interpolation Principles 116 6.2 Polynomial Interpolation 118 6.

4 ix Option Pricing Water Management Bioeconomic Model Solution Algorithms Backward Recursion Function Iteration Policy Iteration Curse of Dimensionality Dynamic Simulation Analysis A Discrete Dynamic Programming Tool Kit Numerical Examples Mine Management Asset Replacement Asset Replacement with Maintenance Option Pricing Water Management Bioeconomic Model 182 Exercises 185 Bibliographie Notes Discrete Time, Continuous State Dynamic Models: Theory and Examples Continuous State Dynamic Programming Euler Conditions Continuous State, Discrete Choice Modeis Asset Replacement Industry Entry and Exit American Option Pricing Continuous State, Continuous Choice Models Economic Growth Renewable Resource Management Nonrenewable Resource Management Water Management Monetary Policy Production-Adjustment Model 204

6.4 Option Pricing 178 7.6.5 Water Management 180 7.6.6 Bioeconomic Model 182 Exercises 185 Bibliographie Notes 188 8 Discrete Time, Continuous State Dynamic Models: Theory and Examples 189 8.

5 8.4.7 Production-Inventory Model Livestock Feeding Dynamic Games Capital-Production Game Income Redistribution Game Marketing Board Game Rational Expectations Models Asset Pricing Model Competitive Storage Government Price Controls 217 Exercises 218 Bibliographie Notes Discrete Time, Continuous State Dynamic Models: Methods Linear-Quadratic Control Bellman Equation Collocation Methods Implementation of the Collocation Method A Continuous State Dynamic Programming Tool Kit Postoptimality Analysis Computational Examples: Discrete Choice Asset Replacement Industry Entry and Exit Computational Examples: Continuous Choice Economic Growth Renewable Resource Management Nonrenewable Resource Management Water Management Monetary Policy Production-Adjustment Model Production-Inventory Model Livestock Feeding Dynamic Game Methods Capital-Production Game Income Redistribution Game Marketing Board Game 286

1 Linear-Quadratic Control 223 9.2 Bellman Equation Collocation Methods 227 9.3 Implementation of the Collocation Method 230 9.4 A Continuous State Dynamic Programming Tool Kit 237 9.

6 xi 9.9 Rational Expectations Methods Asset Pricing Model Competitive Storage Government Price Controls 302 Exercises 306 Bibliographie Notes Continuous Time Models: Theory and Examples Arbitrage-Based Asset Valuation Bond Pricing Black-Scholes Option Pricing Formula Stochastic Volatility Model Exotic Options Multivariate Affine Asset Pricing Model Continuous Action Control Choice of the Discount Rate Euler Equation Methods Bang-Bang Problems Continuous Action Control Examples Nonrenewable Resource Management Neoclassical Growth Model Optimal Renewable Resource Extraction Stochastic Growth Portfolio Choice Production with Adjustment Costs Harvesting a Renewable Resource Sequential Learning Regime Switching Methods Machine Abandonment American Put Option Entry-Exit Impulse Control Asset Replacement Timber Harvesting Storage Management 356

2 Continuous Action Control 320 10.2.1 Choice of the Discount Rate 324 10.2.2 Euler Equation Methods 325 10.2.3 Bang-Bang Problems 327 10.3 Continuous Action Control Examples 328 10.3.1 Nonrenewable Resource Management 328 10.

7 Capacity Choice Cash Management 357 Exercises 358 Appendix loa: Dynamic Programming and Optimal Control Theory 367 Bibliographie Notes Continuous Time Models: Solution Methods Solving Arbitrage Valuation Problems A Simple Bond Pricing Model More General Assets An Asset Pricing Solver Black-Scholes Option Pricing Formula Stochastic Volatility Model American Options Exotic Options Affine Asset Pricing Models Calibration Solving Stochastic Control Problems A Solver for Stochastic Control Problems Postoptimality Analysis Stochastic Control Examples Optimal Growth Renewable Resource Management Production with Adjustment Costs Optimal Fish Harvest Sequential Learning Regime Switching Models Asset Abandonment Optimal Fish Harvest Entry-Exit Impulse Control Asset Replacement 44O Timber Management Storage Management Cash Management 455

1.5 Stochastic Volatility Model 385 11.1.6 American Options 387 11.1.7 Exotic Options 391 11.1.8 Affine Asset Pricing Models 400 11.1.9 Calibration 401 11.2 Solving Stochastic Control Problems 405 11.

8 Optimal Fish Harvest 456 Exercises 450 Appendix HA: Basis Matrices for Multivariate Models 465 Bibliographie Notes 457 Appendix A: Mathematical Background 459 A.l Normed Linear Spaces 459 A.2 Matrix Algebra 462 A.3 Real Analysis 464 A.4 Markov Chains 465 A.5 Continuous Time Mathematics 467 A.5.1 Ito Processes 467 A.5.2 Forward and Backward Equations 470 A.5.3 The Feynman-Kac Equation 473 A.5,4 Geometrie Brownian Motion 475 Bibliographie Notes 476 Appendix B: A MATLAB Primer 477 B.l The Basics 477 B.2 Conditional Statements and Looping 481 B.3 Scripts and Functions 483 B.4 Debugging 488 B.5 Other Data Types 490 B.6 Programming Style 491 References 493 Index 499

5.3 The Feynman-Kac Equation 473 A.5,4 Geometrie Brownian Motion 475 Bibliographie Notes 476 Appendix B: A MATLAB Primer 477 B.l The Basics 477 B.

AN INTRODUCTION TO NUMERICAL METHODS AND ANALYSIS

AN INTRODUCTION TO NUMERICAL METHODS AND ANALYSIS Revised Edition James Epperson Mathematical Reviews BICENTENNIAL 0, 1 8 0 7 z ewiley wu 2007 r71 BICENTENNIAL WILEY-INTERSCIENCE A John Wiley & Sons, Inc.,