Applied computational economics and finance

Contents......Page 8
Preface......Page 16
1.1 Some Apparently Simple Questions......Page 20
1.2 An Alternative Analytic Framework......Page 22
Exercises......Page 23
2 Linear Equations and Computer Basics......Page 26
2.1 L-U Factorization......Page 27
2.2 Gaussian Elimination......Page 29
2.3 Rounding Error......Page 31
2.4 Ill Conditioning......Page 32
2.5 Special Linear Equations......Page 34
2.6 Iterative Methods......Page 35
Exercises......Page 38
Appendix 2A: Computer Arithmetic......Page 39
Appendix 2B: Data Storage......Page 43
Bibliographic Notes......Page 45
3 Nonlinear Equations and Complementarity Problems......Page 48
3.1 Bisection Method......Page 49
3.2 Function Iteration......Page 51
3.3 Newton\'s Method......Page 52
3.4 Quasi-Newton Methods......Page 55
3.5 Problems with Newton Methods......Page 59
3.6 Choosing a Solution Method......Page 61
3.7 Complementarity Problems......Page 63
3.8 Complementarity Methods......Page 66
Exercises......Page 71
Bibliographic Notes......Page 76
4 Finite-Dimensional Optimization......Page 78
4.1 Derivative-Free Methods......Page 79
4.2 Newton-Raphson Method......Page 84
4.3 Quasi-Newton Methods......Page 85
4.4 Line Search Methods......Page 89
4.5 Special Cases......Page 91
4.6 Constrained Optimization......Page 93
Exercises......Page 97
Bibliographic Notes......Page 102
5.1 Newton-Cotes Methods......Page 104
5.2 Gaussian Quadrature......Page 107
5.3 Monte Carlo Integration......Page 109
5.4 Quasi–Monte Carlo Integration......Page 111
5.5 An Integration Tool Kit......Page 113
5.6 Numerical Differentiation......Page 116
5.7 Initial Value Problems......Page 124
Exercises......Page 129
Bibliographic Notes......Page 133
6 Function Approximation......Page 134
6.1 Interpolation Principles......Page 135
6.2 Polynomial Interpolation......Page 137
6.3 Piecewise Polynomial Splines......Page 142
6.4 Piecewise Linear Basis Functions......Page 148
6.5 Multidimensional Interpolation......Page 149
6.6 Choosing an Approximation Method......Page 153
6.7 An Approximation Tool Kit......Page 154
6.8 The Collocation Method......Page 160
6.9 Boundary Value Problems......Page 165
Exercises......Page 168
Bibliographic Notes......Page 171
7.1 Discrete Dynamic Programming......Page 174
7.2.1 Mine Management......Page 176
7.2.2 Asset Replacement......Page 177
7.2.3 Asset Replacement with Maintenance......Page 178
7.2.4 Option Pricing......Page 179
7.2.5 Water Management......Page 180
7.2.6 Bioeconomic Model......Page 181
7.3 Solution Algorithms......Page 182
7.3.1 Backward Recursion......Page 183
7.3.3 Policy Iteration......Page 184
7.3.4 Curse of Dimensionality......Page 185
7.4 Dynamic Simulation Analysis......Page 186
7.5 A Discrete Dynamic Programming Tool Kit......Page 188
7.6.1 Mine Management......Page 191
7.6.2 Asset Replacement......Page 194
7.6.3 Asset Replacement with Maintenance......Page 195
7.6.4 Option Pricing......Page 197
7.6.5 Water Management......Page 199
7.6.6 Bioeconomic Model......Page 201
Exercises......Page 204
Bibliographic Notes......Page 207
8 Discrete Time, Continuous State Dynamic Models: Theory and Examples......Page 208
8.1 Continuous State Dynamic Programming......Page 209
8.2 Euler Conditions......Page 210
8.3.1 Asset Replacement......Page 213
8.3.2 Industry Entry and Exit......Page 214
8.3.3 American Option Pricing......Page 215
8.4.1 Economic Growth......Page 216
8.4.2 Renewable Resource Management......Page 217
8.4.3 Nonrenewable Resource Management......Page 219
8.4.4 Water Management......Page 220
8.4.5 Monetary Policy......Page 221
8.4.6 Production-Adjustment Model......Page 223
8.4.7 Production-Inventory Model......Page 224
8.4.8 Livestock Feeding......Page 226
8.5 Dynamic Games......Page 227
8.5.1 Capital-Production Game......Page 228
8.5.2 Income Redistribution Game......Page 229
8.5.3 Marketing Board Game......Page 230
8.6 Rational Expectations Models......Page 231
8.6.1 Asset Pricing Model......Page 233
8.6.2 Competitive Storage......Page 234
8.6.3 Government Price Controls......Page 236
Exercises......Page 237
Bibliographic Notes......Page 240
9.1 Linear-Quadratic Control......Page 242
9.2 Bellman Equation Collocation Methods......Page 246
9.3 Implementation of the Collocation Method......Page 249
9.4 A Continuous State Dynamic Programming Tool Kit......Page 256
9.5 Postoptimality Analysis......Page 257
9.6.1 Asset Replacement......Page 259
9.6.2 Industry Entry and Exit......Page 262
9.7.1 Economic Growth......Page 265
9.7.2 Renewable Resource Management......Page 269
9.7.3 Nonrenewable Resource Management......Page 272
9.7.4 Water Management......Page 275
9.7.5 Monetary Policy......Page 278
9.7.6 Production-Adjustment Model......Page 283
9.7.7 Production-Inventory Model......Page 285
9.7.8 Livestock Feeding......Page 290
9.8 Dynamic Game Methods......Page 292
9.8.1 Capital-Production Game......Page 298
9.8.2 Income Redistribution Game......Page 302
9.8.3 Marketing Board Game......Page 305
9.9 Rational Expectations Methods......Page 310
9.9.1 Asset Pricing Model......Page 314
9.9.2 Competitive Storage......Page 317
9.9.3 Government Price Controls......Page 321
Exercises......Page 325
Bibliographic Notes......Page 328
10.1 Arbitrage-Based Asset Valuation......Page 330
10.1.1 Bond Pricing......Page 333
10.1.2 Black-Scholes Option Pricing Formula......Page 334
10.1.3 Stochastic Volatility Model......Page 335
10.1.4 Exotic Options......Page 336
10.1.5 Multivariate Affine Asset Pricing Model......Page 338
10.2 Continuous Action Control......Page 339
10.2.1 Choice of the Discount Rate......Page 343
10.2.2 Euler Equation Methods......Page 344
10.2.3 Bang-Bang Problems......Page 346
10.3.1 Nonrenewable Resource Management......Page 347
10.3.2 Neoclassical Growth Model......Page 348
10.3.3 Optimal Renewable Resource Extraction......Page 349
10.3.4 Stochastic Growth......Page 351
10.3.5 Portfolio Choice......Page 352
10.3.6 Production with Adjustment Costs......Page 355
10.3.7 Harvesting a Renewable Resource......Page 356
10.3.8 Sequential Learning......Page 357
10.4 Regime Switching Models......Page 360
10.4.1 Machine Abandonment......Page 362
10.4.3 Entry-Exit......Page 364
10.5 Impulse Control......Page 366
10.5.1 Asset Replacement......Page 373
10.5.2 Timber Harvesting......Page 374
10.5.4 Capacity Choice......Page 375
10.5.5 Cash Management......Page 376
Exercises......Page 377
Appendix 10A: Dynamic Programming and Optimal Control Theory......Page 386
Bibliographic Notes......Page 387
11 Continuous Time Models: Solution Methods......Page 390
11.1 Solving Arbitrage Valuation Problems......Page 391
11.1.1 A Simple Bond Pricing Model......Page 392
11.1.2 More General Assets......Page 394
11.1.3 An Asset Pricing Solver......Page 398
11.1.4 Black-Scholes Option Pricing Formula......Page 401
11.1.5 Stochastic Volatility Model......Page 404
11.1.6 American Options......Page 406
11.1.7 Exotic Options......Page 410
11.1.8 Affine Asset Pricing Models......Page 419
11.1.9 Calibration......Page 420
11.2 Solving Stochastic Control Problems......Page 424
11.2.1 A Solver for Stochastic Control Problems......Page 425
11.2.2 Postoptimality Analysis......Page 428
11.3.1 Optimal Growth......Page 431
11.3.2 Renewable Resource Management......Page 434
11.3.3 Production with Adjustment Costs......Page 436
11.3.4 Optimal Fish Harvest......Page 439
11.3.5 Sequential Learning......Page 442
11.4 Regime Switching Models......Page 447
11.4.1 Asset Abandonment......Page 450
11.4.2 Optimal Fish Harvest......Page 451
11.4.3 Entry-Exit......Page 453
11.5 Impulse Control......Page 456
11.5.1 Asset Replacement......Page 459
11.5.2 Timber Management......Page 460
11.5.3 Storage Management......Page 462
11.5.4 Cash Management......Page 464
11.5.5 Optimal Fish Harvest......Page 465
Exercises......Page 469
Appendix 11A: Basis Matrices for Multivariate Models......Page 474
Bibliographic Notes......Page 476
A.1 Normed Linear Spaces......Page 478
A.2 Matrix Algebra......Page 481
A.3 Real Analysis......Page 483
A.4 Markov Chains......Page 484
A.5.1 Ito Processes......Page 486
A.5.2 Forward and Backward Equations......Page 489
A.5.3 The Feynman-Kac Equation......Page 492
A.5.4 Geometric Brownian Motion......Page 494
Bibliographic Notes......Page 495
B.1 The Basics......Page 496
B.2 Conditional Statements and Looping......Page 500
B.3 Scripts and Functions......Page 502
B.4 Debugging......Page 507
B.5 Other Data Types......Page 509
B.6 Programming Style......Page 510
References......Page 512
C......Page 518
D......Page 521
E......Page 522
G......Page 523
I......Page 524
M......Page 525
O......Page 526
R......Page 527
S......Page 528
W......Page 529