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Mediterranean Journal of Mathematics

, Volume 9, Issue 4, pp 563–574 | Cite as

Vector Risk Functions

  • Alejandro Balbás
  • Raquel Balbás
  • Pedro Jiménez-GuerraEmail author
Article

Abstract

The paper introduces a new notion of vector-valued risk function, a crucial notion in Actuarial and Financial Mathematics. Both deviations and expectation bounded or coherent risk measures are defined and analyzed. The relationships with both scalar and vector risk functions of previous literature are discussed, and it is pointed out that this new approach seems to appropriately integrate several preceding points of view. The framework of the study is the general setting of Banach lattices and Bochner integrable vector-valued random variables. Sub-gradient linked representation theorems and practical examples are provided.

Mathematics Subject Classification (2010)

91B30 91G80 

Keywords

Vector risk function representation theorem dynamic risk measures and other examples 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Alejandro Balbás
    • 1
  • Raquel Balbás
    • 2
  • Pedro Jiménez-Guerra
    • 3
    Email author
  1. 1.University Carlos III of MadridGetafe, (Madrid)Spain
  2. 2.Department of Actuarial and Financial EconomicsUniversity Complutense of MadridPozuelo de Alarcón, (Madrid)Spain
  3. 3.Department of Fundamental MathematicsSpanish Open UniversityMadridSpain

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