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 RudloffEmail author
  • 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 



The authors emphasize that this project benefited from discussions with Frank Heyde (about the primal definition of AV@R) and Andreas Löhne (about the computational part). We are grateful to the referees of a previous version for their constructive remarks. Birgit Rudloff’s research was supported by NSF award DMS-1007938.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Andreas H. Hamel
    • 1
  • Birgit Rudloff
    • 2
    Email author
  • 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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