Springer Proceedings in Mathematics & Statistics

Set Optimization and Applications - The State of the Art

From Set Relations to Set-Valued Risk Measures

Editors: Hamel, A.H., Heyde, F., Löhne, A., Rudloff, B., Schrage, C. (Eds.)

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eBook $129.00
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  • ISBN 978-3-662-48670-2
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Softcover $169.00
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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.

 

Table of contents (11 chapters)

  • A Comparison of Techniques for Dynamic Multivariate Risk Measures

    Feinstein, Zachary (et al.)

    Pages 3-41

  • Nonlinear Scalarizations of Set Optimization Problems with Set Orderings

    Gutiérrez, César (et al.)

    Pages 43-63

  • Set Optimization—A Rather Short Introduction

    Hamel, Andreas H. (et al.)

    Pages 65-141

  • A Survey of Set Optimization Problems with Set Solutions

    Hernández, Elvira

    Pages 143-158

  • Linear Vector Optimization and European Option Pricing Under Proportional Transaction Costs

    Roux, Alet (et al.)

    Pages 159-176

Buy this book

eBook $129.00
price for USA (gross)
  • ISBN 978-3-662-48670-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.00
price for USA
  • ISBN 978-3-662-48668-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $169.00
price for USA
  • ISBN 978-3-662-51139-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

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
Series Volume
151
Copyright
2015
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-48670-2
DOI
10.1007/978-3-662-48670-2
Hardcover ISBN
978-3-662-48668-9
Softcover ISBN
978-3-662-51139-8
Series ISSN
2194-1009
Edition Number
1
Number of Pages
XII, 331
Number of Illustrations and Tables
16 b/w illustrations
Topics