Authors:
- First book on the market to highlight the interval market model in mathematical finance
- Combines several related paths of research into a single source, while providing numerous unpublished results
- Presented in a manner accessible to readers specializing in both mathematics and finance
- Includes many features to clarify concepts and facilitate referencing, such as figures, tables, biographical data, and subject, author, and notation indices
Part of the book series: Static & Dynamic Game Theory: Foundations & Applications (SDGTFA)
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Table of contents (18 chapters)
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Front Matter
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Revisiting Two Classic Results in Dynamic Portfolio Management
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Front Matter
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Revisiting two classical results in dynamic portfolio management
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Hedging in Interval Models
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Front Matter
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Robust-Control Approach to Option Pricing
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Front Matter
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Robust Control Approach to option Pricing
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Game-Theoretic Analysis of Rainbow Options in Incomplete Markets
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Front Matter
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Game-theoretic analysis of rainbow options in incomplete markets
About this book
Toward the late 1990s, several research groups independently began developing new, related theories in mathematical finance. These theories did away with the standard stochastic geometric diffusion “Samuelson” market model (also known as the Black-Scholes model because it is used in that most famous theory), instead opting for models that allowed minimax approaches to complement or replace stochastic methods. Among the most fruitful models were those utilizing game-theoretic tools and the so-called interval market model. Over time, these models have slowly but steadily gained influence in the financial community, providing a useful alternative to classical methods.
A self-contained monograph, The Interval Market Model in Mathematical Finance: Game-Theoretic Methods assembles some of the most important results, old and new, in this area of research. Written by seven of the most prominent pioneers of the interval market model and game-theoretic finance, the work provides a detailed account of several closely related modeling techniques for an array of problems in mathematical economics. The book is divided into five parts, which successively address topics including:
· probability-free Black-Scholes theory;
· fair-price interval of an option;
· representation formulas and fast algorithms for option pricing;
· rainbow options;
· tychastic approach of mathematical finance based upon viability theory.
This book provides a welcome addition to the literature, complementing myriad titles on the market that take a classical approach to mathematical finance. It is a worthwhile resource for researchers in applied mathematics and quantitative finance, and has also been written in a manner accessible to financially-inclined readers with a limited technical background.
Authors and Affiliations
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INRIA Sophia Antipolis-Mediterranee, Sophia Antipolis cedex, France
Pierre Bernhard
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School of Economics and Management, Econometrics and Operations Research, Tilburg University, Tilburg, Netherlands
Jacob C. Engwerda
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, Department of Industrial Engineering, University of Twente, Enschede, Netherlands
Berend Roorda
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, Econometrics and Operations Research, Tilburg University, Tilburg, Netherlands
J.M. Schumacher
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, Department of Statistics, University of Warwick, Warwick, United Kingdom
Vassili Kolokoltsov
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Université Paris Dauphine, Paris Cedex 16, France
Patrick Saint-Pierre
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VIMADES, Paris, France
Jean-Pierre Aubin
Bibliographic Information
Book Title: The Interval Market Model in Mathematical Finance
Book Subtitle: Game-Theoretic Methods
Authors: Pierre Bernhard, Jacob C. Engwerda, Berend Roorda, J.M. Schumacher, Vassili Kolokoltsov, Patrick Saint-Pierre, Jean-Pierre Aubin
Series Title: Static & Dynamic Game Theory: Foundations & Applications
DOI: https://doi.org/10.1007/978-0-8176-8388-7
Publisher: Birkhäuser New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2013
Hardcover ISBN: 978-0-8176-8387-0Published: 14 December 2012
Softcover ISBN: 978-1-4899-8580-4Published: 28 January 2015
eBook ISBN: 978-0-8176-8388-7Published: 14 December 2012
Series ISSN: 2363-8516
Series E-ISSN: 2363-8524
Edition Number: 1
Number of Pages: XVI, 348
Topics: Game Theory, Economics, Social and Behav. Sciences, Game Theory, Quantitative Finance, Economic Theory/Quantitative Economics/Mathematical Methods, Applications of Mathematics