The authoritative guide to modeling and solving complex problems with linear programming—extensively revised, expanded, and updated The only book to treat both linear programming techniques and ...network flows under one cover, Linear Programming and Network Flows, Fourth Edition has been completely updated with the latest developments on the topic. This new edition continues to successfully emphasize modeling concepts, the design and analysis of algorithms, and implementation strategies for problems in a variety of fields, including industrial engineering, management science, operations research, computer science, and mathematics. The book begins with basic results on linear algebra and convex analysis, and a geometrically motivated study of the structure of polyhedral sets is provided. Subsequent chapters include coverage of cycling in the simplex method, interior point methods, and sensitivity and parametric analysis. Newly added topics in the Fourth Edition include: * The cycling phenomenon in linear programming and the geometry of cycling * Duality relationships with cycling * Elaboration on stable factorizations and implementation strategies * Stabilized column generation and acceleration of Benders and Dantzig-Wolfe decomposition methods * Line search and dual ascent ideas for the out-of-kilter algorithm * Heap implementation comments, negative cost circuit insights, and additional convergence analyses for shortest path problems The authors present concepts and techniques that are illustrated by numerical examples along with insights complete with detailed mathematical analysis and justification. An emphasis is placed on providing geometric viewpoints and economic interpretations as well as strengthening the understanding of the fundamental ideas. Each chapter is accompanied by Notes and References sections that provide historical developments in addition to current and future trends. Updated exercises allow readers to test their comprehension of the presented material, and extensive references provide resources for further study. Linear Programming and Network Flows, Fourth Edition is an excellent book for linear programming and network flow courses at the upper-undergraduate and graduate levels. It is also a valuable resource for applied scientists who would like to refresh their understanding of linear programming and network flow techniques.
Stochastic Finance Föllmer, Hans; Schied, Alexander
2011, 2011-01-28, 20110101
eBook
This is the third, revised and extended edition of the classical introduction to the mathematics of finance, based on stochastic models in discrete time. In the first part of the book simple ...one-period models are studied, in the second part the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Due to the strong appeal and wide use of this book, it is now available as a textbook with exercises. It will be of value for a broad community of students and researchers. It may serve as basis for graduate courses and be also interesting for those who work in the financial industry and want to get an idea about the mathematical methods of risk assessment .Hans Föllmer, Humboldt-Universität zu Berlin, Germany; Alexander Schied, University of Mannheim, Germany.
Originally published in 2003,Mathematical Techniques in Financehas become a standard textbook for master's-level finance courses containing a significant quantitative element while also being ...suitable for finance PhD students. This fully revised second edition continues to offer a carefully crafted blend of numerical applications and theoretical grounding in economics, finance, and mathematics, and provides plenty of opportunities for students to practice applied mathematics and cutting-edge finance. Ales Cerný mixes tools from calculus, linear algebra, probability theory, numerical mathematics, and programming to analyze in an accessible way some of the most intriguing problems in financial economics. The textbook is the perfect hands-on introduction to asset pricing, optimal portfolio selection, risk measurement, and investment evaluation.
The new edition includes the most recent research in the area of incomplete markets and unhedgeable risks, adds a chapter on finite difference methods, and thoroughly updates all bibliographic references. Eighty figures, over seventy examples, twenty-five simple ready-to-run computer programs, and several spreadsheets enhance the learning experience. All computer codes have been rewritten using MATLAB and online supplementary materials have been completely updated.
A standard textbook for graduate finance coursesIntroduction to asset pricing, portfolio selection, risk measurement, and investment evaluationDetailed examples and MATLAB codes integrated throughout the textExercises and summaries of main points conclude each chapter
This important book provides information necessary for those dealing with stochastic calculus and pricing in the models of financial markets operating under uncertainty; introduces the reader to the ...main concepts, notions and results of stochastic financial mathematics; and develops applications of these results to various kinds of calculations required in financial engineering. It also answers the requests of teachers of financial mathematics and engineering by making a bias towards probabilistic and statistical ideas and the methods of stochastic calculus in the analysis of market risks.
