Optimization Methods in Finance

Full treatment, from model formulation to computational implementation, of optimization techniques that solve central problems in finance.

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.