Mathematics and Financial Economics

, Volume 5, Issue 1, pp 1–28

Set-valued risk measures for conical market models


    • Department of Mathematical SciencesYeshiva University
  • Frank Heyde
    • Institute of MathematicsUniversity Halle-Wittenberg
  • Birgit Rudloff
    • Princeton University, ORFE

DOI: 10.1007/s11579-011-0047-0

Cite this article as:
Hamel, A.H., Heyde, F. & Rudloff, B. Math Finan Econ (2011) 5: 1. doi:10.1007/s11579-011-0047-0


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.


Set-valued risk measuresCoherent risk measuresConical market modelLegendre–Fenchel transformConvex dualityTransaction costsSuper-hedging

Mathematics Subject Classification (2000)


JEL Classification


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© Springer-Verlag 2011