Mathematics and Financial Economics

, Volume 5, Issue 1, pp 1–28 | Cite as

Set-valued risk measures for conical market models

Article

Abstract

Set-valued risk measures on \({L^p_d}\) with 0 ≤ p ≤ ∞ for conical market models are defined, primal and dual representation results are given. The collection of initial endowments which allow to super-hedge a multivariate claim are shown to form the values of a set-valued sublinear (coherent) risk measure. Scalar risk measures with multiple eligible assets also turn out to be a special case within the set-valued framework.

Keywords

Set-valued risk measures Coherent risk measures Conical market model Legendre–Fenchel transform Convex duality Transaction costs Super-hedging 

Mathematics Subject Classification (2000)

91B30 46A20 46N10 26E25 

JEL Classification

C65 D81 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Andreas H. Hamel
    • 1
  • Frank Heyde
    • 2
  • Birgit Rudloff
    • 3
  1. 1.Department of Mathematical SciencesYeshiva UniversityNew YorkUSA
  2. 2.Institute of MathematicsUniversity Halle-WittenbergHalleGermany
  3. 3.Princeton University, ORFEPrincetonUSA

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