Part I Introduction 1

1 Overview of Optimization Models 3

2 Linear Programming: Theory and Algorithms11

3 Linear Programming Models:Asset–Liability Management 35

4 Linear Programming Models: Arbitrage andAsset Pricing 53

Part II Single-Period Models 69

5 Quadratic Programming: Theory andAlgorithms 71

6 Quadratic Programming Models:Mean–Variance Optimization 90

7 Sensitivity of Mean–Variance Models toInput Estimation 124

8 Mixed Integer Programming: Theory andAlgorithms 140

9Mixed Integer Programming Models:Portfolios with Combinatorial Constraints 161

10 Stochastic Programming: Theory andAlgorithms 173

11 Stochastic Programming Models: RiskMeasures 181

Part III Multi-Period Models 195

12 Multi-Period Models: Simple Examples 197

13 Dynamic Programming: Theory andAlgorithms 212

14 Dynamic Programming Models: Multi-PeriodPortfolio Optimization 225

15 Dynamic Programming Models: the BinomialPricing Model 238

16 Multi-Stage Stochastic Programming 248

17 Stochastic Programming Models:Asset–Liability Management 262

Part IV Other Optimization Techniques 275

18 Conic Programming: Theory and Algorithms277

19 Robust Optimization 289 19.1 UncertaintySets 289

20 Nonlinear Programming: Theory andAlgorithms 305

Appendices 321

References 327

Index 334