Description
Optimization models play an increasingly important role in financial decisions. This is the first textbook devoted to explaining how recent advances in optimization models, methods and software can be applied to solve problems in computational finance more efficiently and accurately. Chapters discussing the theory and efficient solution methods for all major classes of optimization problems alternate with chapters illustrating their use in modeling problems of mathematical finance. The reader is guided through topics such as volatility estimation, portfolio optimization problems and constructing an index fund, using techniques such as nonlinear optimization models, quadratic programming formulations and integer programming models respectively. The book is based on Master's courses in financial engineering and comes with worked examples, exercises and case studies. It will be welcomed by applied mathematicians, operational researchers and others who work in mathematical and computational finance and who are seeking a text for self-learning or for use with courses.
Table of Contents
1. Introduction; 2. Linear programming: theory and algorithms; 3. LP models: asset/liability cash flow matching; 4. LP models: asset pricing and arbitrage; 5. Nonlinear programming: theory and algorithms; 6. NLP volatility estimation; 7. Quadratic programming: theory and algorithms; 8. QP models: portfolio optimization; 9. Conic optimization tools; 10. Conic optimization models in finance; 11. Integer programming: theory and algorithms; 12. IP models: constructing an index fund; 13. Dynamic programming methods; 14. DP models: option pricing; 15. DP models: structuring asset backed securities; 16. Stochastic programming: theory and algorithms; 17. SP models: value-at-risk; 18. SP models: asset/liability management; 19. Robust optimization: theory and tools; 20. Robust optimization models in finance; Appendix A. Convexity; Appendix B. Cones; Appendix C. A probability primer; Appendix D. The revised simplex method; Bibliography; Index.
