Mathematics and Financial Economics

, Volume 7, Issue 2, pp 229–246

Set-valued average value at risk and its computation

  • Andreas H. Hamel
  • Birgit Rudloff
  • Mihaela Yankova
Article

DOI: 10.1007/s11579-013-0094-9

Cite this article as:
Hamel, A.H., Rudloff, B. & Yankova, M. Math Finan Econ (2013) 7: 229. doi:10.1007/s11579-013-0094-9
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Abstract

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.

Keywords

Average value at riskSet-valued risk measuresCoherent risk measuresTransaction costsBenson’s algorithm

Mathematics Subject Classification (2000)

91B3046N1026E2546A20

JEL Classifications

C61 G32

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