Optimization methods play a central role in financial modeling. This textbook is devoted to explaining how state-of-the-art optimization theory, algorithms, and software can be used to efficiently solve problems in computational finance. It discusses some classical mean-variance portfolio optimization models as well as more modern developments such as models for optimal trade execution and dynamic portfolio allocation with transaction costs and taxes. Chapters discussing the theory and efficient solution methods for the main classes of optimization problems alternate with chapters discussing their use in the modeling and solution of central problems in mathematical finance. This book will be interesting and useful for students, academics, and practitioners with a background in mathematics, operations research, or financial engineering. The second edition includes new examples and exercises as well as a more detailed discussion of mean-variance optimization, multi-period models, and additional material to highlight the relevance to finance.
Part I. Introduction:
1. Overview of optimization models
2. Linear programming: theory and algorithms
3. Linear programming models: asset-liability management
4. Linear programming models: arbitrage and asset pricing
Part II. Single-Period Models:
5. Quadratic programming: theory and algorithms
6. Quadratic programming models: mean-variance optimization
7. Sensitivity of mean-variance models to input estimation
8. Mixed integer programming: theory and algorithms
9. Mixed integer programming models: portfolios with combinatorial constraints
10. Stochastic programming: theory and algorithms
11. Stochastic programming models: risk measures
Part III. Multi-Period Models:
12. Multi-period models: simple examples
13. Dynamic programming: theory and algorithms
14. Dynamic programming models: multi-period portfolio optimization
15. Dynamic programming models: the binomial pricing model
16. Multi-stage stochastic programming
17. Stochastic programming models: asset-liability management
Part IV. Other Optimization Techniques:
18. Conic programming: theory and algorithms
19. Robust optimization
20. Nonlinear programming: theory and algorithms
Appendix
References
Index.
