Mathematics and Financial Economics

, Volume 7, Issue 2, pp 229–246 | Cite as

Set-valued average value at risk and its computation

  • Andreas H. Hamel
  • Birgit Rudloff
  • Mihaela Yankova


New versions of the set-valued average value at risk for multivariate risks are introduced by generalizing the well-known certainty equivalent representation to the set-valued case. The first ’regulator’ version is independent from any market model whereas the second version, called the market extension, takes trading opportunities into account. Essential properties of both versions are proven and an algorithmic approach is provided which admits to compute the values of both versions over finite probability spaces. Several examples illustrate various features of the theoretical constructions.


Average value at risk Set-valued risk measures Coherent risk measures Transaction costs Benson’s algorithm 

Mathematics Subject Classification (2000)

91B30 46N10 26E25 46A20 

JEL Classifications

C61  G32 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Andreas H. Hamel
    • 1
  • Birgit Rudloff
    • 2
  • Mihaela Yankova
    • 3
  1. 1.Department of Mathematical SciencesYeshiva UniversityNew YorkUSA
  2. 2.ORFE, BCFPrinceton UniversityPrincetonUSA
  3. 3.Barclays CapitalNew YorkUSA

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