Set-valued risk measures for conical market models

@article{Hamel2010SetvaluedRM,
title={Set-valued risk measures for conical market models},
author={Andreas H. Hamel and F. Heyde and B. Rudloff},
journal={Mathematics and Financial Economics},
year={2010},
volume={5},
pages={1-28}
}

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.