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.

This volume contains the papers selected for presentation at IPCO VII, the Seventh Conference on Integer Programming and Combinatorial Optimization, Graz, Austria, June9{11,1999.Thismeetingisaforumforresearchersandpr- titioners working on various aspects of integer programming and combinatorial optimization. The aim is to present recent developments in theory, compu- tion, and applications of integer programming and combinatorial optimization. Topics include, but are not limited to: approximation algorithms, branch and bound algorithms, computational biology, computational complexity, compu- tional geometry, cutting plane algorithms, diophantine equations, geometry of numbers, graph and network algorithms, integer programming, matroids and submodular functions, on-line algorithms, polyhedral combinatorics, scheduling theory and algorithms, and semide nite programs. IPCO was established in 1988 when the rst IPCO program committee was formed. IPCO I took place in Waterloo (Canada) in 1990, IPCO II was held in Pittsburgh (USA) in 1992, IPCO III in Erice (Italy) 1993, IPCO IV in Cop- hagen (Denmark) 1995, IPCO V in Vancouver (Canada) 1996, and IPCO VI in Houston (USA) 1998. IPCO is held every year in which no MPS (Mathematical Programming Society) International Symposium takes place: 1990, 1992, 1993, 1995,1996,1998,1999,2001,2002,2004,2005,2007,2008: ::::: Since the MPS meeting is triennial, IPCO conferences are held twice in everythree-year period. As a rule, in even years IPCO is held somewhere in Northern America, and in odd years it is held somewhere in Europe. In response to the call for papers for IPCO 99, the program committee - ceived99submissions, indicatingastrongandgrowinginterestintheconfere