Set Optimization and Applications - The State of the Art

From Set Relations to Set-Valued Risk Measures

  • Andreas H Hamel
  • Frank Heyde
  • Andreas Löhne
  • Birgit Rudloff
  • Carola Schrage
Conference proceedings

Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 151)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Surveys

    1. Front Matter
      Pages 1-1
    2. Zachary Feinstein, Birgit Rudloff
      Pages 3-41
    3. César Gutiérrez, Bienvenido Jiménez, Vicente Novo
      Pages 43-63
    4. Andreas H. Hamel, Frank Heyde, Andreas Löhne, Birgit Rudloff, Carola Schrage
      Pages 65-141
  3. Special Topics

    1. Front Matter
      Pages 177-177
    2. Patrick Cheridito, Michael Kupper, Nicolas Vogelpoth
      Pages 179-211
    3. Giovanni P. Crespi, Carola Schrage
      Pages 213-247
    4. Yuri Kabanov, Emmanuel Lepinette
      Pages 275-291
    5. Daishi Kuroiwa
      Pages 293-311

About these proceedings


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.



49-06, 90-06, 91Gxx, 06-xx, 49J53, 49N15, 49M29 complete lattice approach duality multi-criteria decision making set optimization set-valued risk measures scalarization methods

Editors and affiliations

  • Andreas H Hamel
    • 1
  • Frank Heyde
    • 2
  • Andreas Löhne
    • 3
  • Birgit Rudloff
    • 4
  • Carola Schrage
    • 5
  1. 1.Free University Bozen-BolzanoBozen-BolzanoItaly
  2. 2.FreibergUniversity of Technology BergakademieFreibergGermany
  3. 3.Friedrich-Schiller-University JenaJenaGermany
  4. 4.and BusinessVienna University of EconomicsViennaAustria
  5. 5.Free University Bozen-BolzanoBozen-BolzanoItaly

Bibliographic information