Numerical Methods and Optimization in Finance

Manfred Gilli is Professor emeritus at the Geneva School of Economics and Management at the University of Geneva, Switzerland, where he has taught numerical methods in economics and finance. He is also a Faculty member of the Swiss Finance Institute, a member of the Advisory Board of Computational Statistics and Data Analysis, and a member of the editorial board of Computational Economics. He formerly served as president of the Society for Computational Economics. Dietmar Maringer is Professor of Computational Economics and Finance at the University of Basel, Switzerland, and a faculty member at the Geneva School of Economics and Management. His research interests include non-deterministic methods such as heuristic optimization and simulations, computational learning, and empirical methods, typically with applications in trading, risk, and financial management. Enrico Schumann holds a Ph.D. in econometrics, an MSC in economics, and a BA in economics and law. He has written on numerical methods and their application in finance, with a focus on asset allocation. His research interests include quantitative investment strategies and portfolio construction, computationally-intensive methods (in particular, optimization), and automated data processing and analysis.

• 1. IntroductionI. Fundamentals2. Numerical Analysis in a Nutshell3. Linear Equations and Least Squares Problems4. Finite Difference Methods5. Binomial TreesII. Simulation6. Generating Random Numbers7. Modeling Dependencies8. A Gentle Introduction to Financial Simulation9. Financial Simulation at Work: Some Case StudiesIII. Optimization10. Optimization Problems in Finance11. Basic Methods12. Heuristic Methods in a Nutshell13.: Heuristic Methods: A Tutorial14. Portfolio Optimization15. Backtesting Investment Strategies16. Econometric Models17. Calibrating Option Pricing Models