Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 151)
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About this book
This volume presents five surveys with extensive bibliographies and six original contributions on set optimization and its applications in mathematical finance and game theory. The topics range from more conventional approaches that look for minimal/maximal elements with respect to vector orders or set relations, to the new complete-lattice approach that comprises a coherent solution concept for set optimization problems, along with existence results, duality theorems, optimality conditions, variational inequalities and theoretical foundations for algorithms. Modern approaches to scalarization methods can be found as well as a fundamental contribution to conditional analysis. The theory is tailor-made for financial applications, in particular risk evaluation and [super-]hedging for market models with transaction costs, but it also provides a refreshing new perspective on vector optimization. There is no comparable volume on the market, making the book an invaluable resource for researchers working in vector optimization and multi-criteria decision-making, mathematical finance and economics as well as [set-valued] variational analysis.
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Table of contents (11 papers)
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Front Matter
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Surveys
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Front Matter
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Special Topics
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Front Matter
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Editors and Affiliations
Bibliographic Information
Book Title: Set Optimization and Applications - The State of the Art
Book Subtitle: From Set Relations to Set-Valued Risk Measures
Editors: Andreas H Hamel, Frank Heyde, Andreas Löhne, Birgit Rudloff, Carola Schrage
Series Title: Springer Proceedings in Mathematics & Statistics
DOI: https://doi.org/10.1007/978-3-662-48670-2
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2015
Hardcover ISBN: 978-3-662-48668-9Published: 22 November 2015
Softcover ISBN: 978-3-662-51139-8Published: 23 August 2016
eBook ISBN: 978-3-662-48670-2Published: 21 November 2015
Series ISSN: 2194-1009
Series E-ISSN: 2194-1017
Edition Number: 1
Number of Pages: XII, 331
Number of Illustrations: 16 b/w illustrations
Topics: Calculus of Variations and Optimal Control; Optimization, Quantitative Finance, Order, Lattices, Ordered Algebraic Structures, Continuous Optimization