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Table of contents :
Contents......Page 3
Preface......Page 8
Overview of Optimization Models......Page 11
Types of Optimization Models......Page 12
Solution to Optimization Problems......Page 15
Financial Optimization Models......Page 16
Notes......Page 18
Linear Programming......Page 19
Graphical Interpretation of a Two-Variable Example......Page 23
Numerical Linear Programming Solvers......Page 24
Sensitivity Analysis......Page 25
*Duality......Page 28
*Optimality Conditions......Page 31
*Algorithms for Linear Programming......Page 32
Notes......Page 38
Exercises......Page 39
Dedication......Page 43
Immunization......Page 46
Some Practical Details about Bonds......Page 49
Other Cash Flow Problems......Page 52
Exercises......Page 55
Case Study......Page 59
Arbitrage Detection in the Foreign Exchange Market......Page 61
The Fundamental Theorem of Asset Pricing......Page 63
One-Period Binomial Pricing Model......Page 64
Static Arbitrage Bounds......Page 67
Tax Clientele Effects in Bond Portfolio Management......Page 71
Exercises......Page 73
--- Single-Period Models......Page 77
Quadratic Programming......Page 78
Numerical Quadratic Programming Solvers......Page 81
Sensitivity Analysis......Page 82
*Duality and Optimality Conditions......Page 83
*Algorithms......Page 88
Applications to Machine Learning......Page 91
Exercises......Page 94
Portfolio Return......Page 97
Markowitz Mean–Variance (Basic Model)......Page 98
Analytical Solutions to Basic Mean–Variance Models......Page 102
More General Mean–Variance Models......Page 106
Portfolio Management Relative to a Benchmark......Page 110
Estimation of Inputs to Mean–Variance Models......Page 113
Performance Analysis......Page 119
Exercises......Page 122
Case Studies......Page 128
Sensitivity of Mean–Variance Models to Input Estimation......Page 131
Black–Litterman Model......Page 133
Shrinkage Estimation......Page 136
Resampled Efficiency......Page 138
Robust Optimization......Page 139
Other Diversification Approaches......Page 140
Exercises......Page 142
Mixed Integer Programming......Page 147
Numerical Mixed Integer Programming Solvers......Page 150
Relaxations and Duality......Page 152
Algorithms for Solving Mixed Integer Programs......Page 157
Exercises......Page 164
Combinatorial Auctions......Page 168
The Lockbox Problem......Page 170
Constructing an Index Fund......Page 172
Cardinality Constraints......Page 174
Minimum Position Constraints......Page 175
Exercises......Page 176
Case Study......Page 178
Examples of Stochastic Optimization Models......Page 180
Two-Stage Stochastic Optimization......Page 181
Linear Two-Stage Stochastic Programming......Page 182
Scenario Optimization......Page 183
*The L-Shaped Method......Page 184
Exercises......Page 186
Risk Measures......Page 188
A Key Property of CVaR......Page 192
Portfolio Optimization with CVaR......Page 193
Exercises......Page 197
--- Multi-Period Models......Page 201
The Kelly Criterion......Page 202
Dynamic Portfolio Optimization......Page 203
Execution Costs......Page 206
Exercises......Page 214
Some Examples......Page 217
Model of a Sequential System (Deterministic Case)......Page 219
Bellman’s Principle of Optimality......Page 220
Linear–Quadratic Regulator......Page 221
Sequential Decision Problem with Infinite Horizon......Page 223
Linear–Quadratic Regulator with Infinite Horizon......Page 224
Model of Sequential System (Stochastic Case)......Page 226
Exercises......Page 227
Utility of Terminal Wealth......Page 230
Optimal Consumption and Investment......Page 232
Dynamic Trading with Predictable Returns and Transaction Costs......Page 233
Dynamic Portfolio Optimization with Taxes......Page 235
Exercises......Page 239
Option Pricing......Page 243
Option Pricing in Continuous Time......Page 249
Specifying the Model Parameters......Page 250
Exercises......Page 251
Multi-Stage Stochastic Programming......Page 253
Scenario Optimization......Page 255
Scenario Generation......Page 260
Exercises......Page 264
Asset–Liability Management......Page 267
The Case of an Insurance Company......Page 268
Option Pricing via Stochastic Programming......Page 270
Synthetic Options......Page 275
Exercises......Page 278
--- Other Optimization Techniques......Page 279
Conic Programming......Page 280
Duality and Optimality Conditions......Page 285
Algorithms......Page 287
Exercises......Page 290
Uncertainty Sets......Page 292
Different Flavors of Robustness......Page 293
Techniques for Solving Robust Optimization Models......Page 297
Some Robust Optimization Models in Finance......Page 300
Exercises......Page 305
Nonlinear Programming......Page 308
Optimality Conditions......Page 309
Algorithms......Page 311
Estimating a Volatility Surface......Page 318
Exercises......Page 322
A.1 Matrices and Vectors......Page 324
A.2 Convex Sets and Convex Functions......Page 325
A.3 Calculus of Variations: the Euler Equation......Page 326
Refs......Page 328
Index......Page 335
Gérard Cornuéjols, Javier Peña, Reha Tütüncü - Optimization Methods .pdf
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