Article

Mathematics and Financial Economics

, Volume 5, Issue 1, pp 1-28

Set-valued risk measures for conical market models

  • Andreas H. HamelAffiliated withDepartment of Mathematical Sciences, Yeshiva University Email author 
  • , Frank HeydeAffiliated withInstitute of Mathematics, University Halle-Wittenberg
  • , Birgit RudloffAffiliated withPrinceton University, ORFE

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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