Set-valued risk measures for conical market models

2010/11/27 by Andreas H. Hamel, Frank Heyde, Birgit Rudloff · 3 citations
Economics, Econometrics and Finance · #q-fin.RM #msc:91B30 #msc:46A20 #msc:46N10 #msc:26E25

paper · pdf

published as Mathematics and Financial Economics 5 (1), 1 - 28, (2011)

arxiv created 2010/11/27 · arxiv updated 2014/05/22

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.

Cited by

• Geometrically convex return risk measures on AM-algebras
• Dual Representation of Robust Risk Measures and Uncertainty Sets
• Set-valued conditional functionals of random sets

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• Set-valued Star-Shaped Risk Measures
• Multivariate risk measures: a constructive approach based on selections
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• Multivariate risks and depth-trimmed regions
• Measuring risk with multiple eligible assets