Applied Computational Economics and Finance

Applied Computational Economics and Finance

by Mario J. Miranda, Paul L. Fackler
     
 

ISBN-10: 0262134209

ISBN-13: 9780262134200

Pub. Date: 08/20/2004

Publisher: MIT Press

This book presents a variety of computational methods used to solve dynamic problems in economics and finance. It emphasizes practical numerical methods rather than mathematical proofs and focuses on techniques that apply directly to economic analyses. The examples are drawn from a wide range of subspecialties of economics and finance, with particular emphasis on

Overview

This book presents a variety of computational methods used to solve dynamic problems in economics and finance. It emphasizes practical numerical methods rather than mathematical proofs and focuses on techniques that apply directly to economic analyses. The examples are drawn from a wide range of subspecialties of economics and finance, with particular emphasis on problems in agricultural and resource economics, macroeconomics, and finance. The book's Web site provides an extensive Web site library of computer utilities and demonstration programs.

The book is divided into two parts. The first part develops basic numerical methods, including linear and nonlinear equation methods, complementarity methods, finite-dimensional optimization, numerical integration and differentiation, and function approximation. The second part presents methods for solving dynamic stochastic models in economics and finance, including dynamic programming, rational expectations, and arbitrage pricing models in discrete and continuous time. The book uses MATLAB to illustrate the algorithms and includes a utilities toolbox to help readers develop their own computational economics applications.

Product Details

ISBN-13:
9780262134200
Publisher:
MIT Press
Publication date:
08/20/2004
Pages:
528
Product dimensions:
7.00(w) x 9.00(h) x 0.68(d)
Age Range:
18 Years

Table of Contents

Prefacexv
1Introduction1
1.1Some Apparently Simple Questions1
1.2An Alternative Analytic Framework3
Exercises4
2Linear Equations and Computer Basics7
2.1L-U Factorization8
2.2Gaussian Elimination10
2.3Rounding Error12
2.4Ill Conditioning13
2.5Special Linear Equations15
2.6Iterative Methods16
Exercises19
Appendix 2AComputer Arithmetic20
Appendix 2BData Storage24
Bibliographic Notes26
3Nonlinear Equations and Complementarity Problems29
3.1Bisection Method30
3.2Function Iteration32
3.3Newton's Method33
3.4Quasi-Newton Methods36
3.5Problems with Newton Methods40
3.6Choosing a Solution Method42
3.7Complementarity Problems44
3.8Complementarity Methods47
Exercises52
Bibliographic Notes57
4Finite-Dimensional Optimization59
4.1Derivative-Free Methods60
4.2Newton-Raphson Method65
4.3Quasi-Newton Methods66
4.4Line Search Methods70
4.5Special Cases72
4.6Constrained Optimization74
Exercises78
Bibliographic Notes83
5Numerical Integration and Differentiation85
5.1Newton-Cotes Methods85
5.2Gaussian Quadrature88
5.3Monte Carlo Integration90
5.4Quasi-Monte Carlo Integration92
5.5An Integration Tool Kit94
5.6Numerical Differentiation97
5.7Initial Value Problems105
Exercises110
Bibliographic Notes114
6Function Approximation115
6.1Interpolation Principles116
6.2Polynomial Interpolation118
6.3Piecewise Polynomial Splines123
6.4Piecewise Linear Basis Functions129
6.5Multidimensional Interpolation130
6.6Choosing an Approximation Method134
6.7An Approximation Tool Kit135
6.8The Collocation Method141
6.9Boundary Value Problems146
Exercises149
Bibliographic Notes152
7Discrete Time, Discrete State Dynamic Models155
7.1Discrete Dynamic Programming155
7.2Economic Examples157
7.2.1Mine Management157
7.2.2Asset Replacement158
7.2.3Asset Replacement with Maintenance159
7.2.4Option Pricing160
7.2.5Water Management161
7.2.6Bioeconomic Model162
7.3Solution Algorithms163
7.3.1Backward Recursion164
7.3.2Function Iteration165
7.3.3Policy Iteration165
7.3.4Curse of Dimensionality166
7.4Dynamic Simulation Analysis167
7.5A Discrete Dynamic Programming Tool Kit169
7.6Numerical Examples172
7.6.1Mine Management172
7.6.2Asset Replacement175
7.6.3Asset Replacement with Maintenance176
7.6.4Option Pricing178
7.6.5Water Management180
7.6.6Bioeconomic Model182
Exercises185
Bibliographic Notes188
8Discrete Time, Continuous State Dynamic Models: Theory and Examples189
8.1Continuous State Dynamic Programming190
8.2Euler Conditions191
8.3Continuous State, Discrete Choice Models194
8.3.1Asset Replacement194
8.3.2Industry Entry and Exit195
8.3.3American Option Pricing196
8.4Continuous State, Continuous Choice Models197
8.4.1Economic Growth197
8.4.2Renewable Resource Management198
8.4.3Nonrenewable Resource Management200
8.4.4Water Management201
8.4.5Monetary Policy202
8.4.6Production-Adjustment Model204
8.4.7Production-Inventory Model205
8.4.8Livestock Feeding207
8.5Dynamic Games208
8.5.1Capital-Production Game209
8.5.2Income Redistribution Game210
8.5.3Marketing Board Game211
8.6Rational Expectations Models212
8.6.1Asset Pricing Model214
8.6.2Competitive Storage215
8.6.3Government Price Controls217
Exercises218
Bibliographic Notes221
9Discrete Time, Continuous State Dynamic Models: Methods223
9.1Linear-Quadratic Control223
9.2Bellman Equation Collocation Methods227
9.3Implementation of the Collocation Method230
9.4A Continuous State Dynamic Programming Tool Kit237
9.5Postoptimality Analysis238
9.6Computational Examples: Discrete Choice240
9.6.1Asset Replacement240
9.6.2Industry Entry and Exit243
9.7Computational Examples: Continuous Choice246
9.7.1Economic Growth246
9.7.2Renewable Resource Management250
9.7.3Nonrenewable Resource Management253
9.7.4Water Management256
9.7.5Monetary Policy259
9.7.6Production-Adjustment Model264
9.7.7Production-Inventory Model266
9.7.8Livestock Feeding271
9.8Dynamic Game Methods273
9.8.1Capital-Production Game279
9.8.2Income Redistribution Game283
9.8.3Marketing Board Game286
9.9Rational Expectations Methods291
9.9.1Asset Pricing Model295
9.9.2Competitive Storage298
9.9.3Government Price Controls302
Exercises306
Bibliographic Notes309
10Continuous Time Models: Theory and Examples311
10.1Arbitrage-Based Asset Valuation311
10.1.1Bond Pricing314
10.1.2Black-Scholes Option Pricing Formula315
10.1.3Stochastic Volatility Model316
10.1.4Exotic Options317
10.1.5Multivariate Affine Asset Pricing Model319
10.2Continuous Action Control320
10.2.1Choice of the Discount Rate324
10.2.2Euler Equation Methods325
10.2.3Bang-Bang Problems327
10.3Continuous Action Control Examples328
10.3.1Nonrenewable Resource Management328
10.3.2Neoclassical Growth Model329
10.3.3Optimal Renewable Resource Extraction330
10.3.4Stochastic Growth332
10.3.5Portfolio Choice333
10.3.6Production with Adjustment Costs336
10.3.7Harvesting a Renewable Resource337
10.3.8Sequential Learning338
10.4Regime Switching Methods342
10.4.1Machine Abandonment343
10.4.2American Put Option345
10.4.3Entry-Exit345
10.5Impulse Control347
10.5.1Asset Replacement354
10.5.2Timber Harvesting355
10.5.3Storage Management356
10.5.4Capacity Choice356
10.5.5Cash Management357
Exercises358
Appendix 10ADynamic Programming and Optimal Control Theory367
Bibliographic Notes368
11Continuous Time Models: Solution Methods371
11.1Solving Arbitrage Valuation Problems372
11.1.1A Simple Bond Pricing Model373
11.1.2More General Assets375
11.1.3An Asset Pricing Solver379
11.1.4Black-Scholes Option Pricing Formula382
11.1.5Stochastic Volatility Model385
11.1.6American Options387
11.1.7Exotic Options391
11.1.8Affine Asset Pricing Models400
11.1.9Calibration401
11.2Solving Stochastic Control Problems405
11.2.1A Solver for Stochastic Control Problems406
11.2.2Postoptimality Analysis409
11.3Stochastic Control Examples412
11.3.1Optimal Growth412
11.3.2Renewable Resource Management415
11.3.3Production with Adjustment Costs417
11.3.4Optimal Fish Harvest420
11.3.5Sequential Learning423
11.4Regime Switching Models428
11.4.1Asset Abandonment431
11.4.2Optimal Fish Harvest432
11.4.3Entry-Exit434
11.5Impulse Control437
11.5.1Asset Replacement440
11.5.2Timber Management441
11.5.3Storage Management443
11.5.4Cash Management455
11.5.5Optimal Fish Harvest456
Exercises450
Appendix 11 ABasis Matrices for Multivariate Models465
Bibliographic Notes457
Appendix AMathematical Background459
A.1Normed Linear Spaces459
A.2Matrix Algebra462
A.3Real Analysis464
A.4Markov Chains465
A.5Continuous Time Mathematics467
A.5.1Ito Processes467
A.5.2Forward and Backward Equations470
A.5.3The Feynman-Kac Equation473
A.5.4Geometric Brownian Motion475
Bibliographic Notes476
Appendix BA Matlab Primer477
B.1The Basics477
B.2Conditional Statements and Looping481
B.3Scripts and Functions483
B.4Debugging488
B.5Other Data Types490
B.6Programming Style491
References493
Index499

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