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.
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Hamel, A.H., Heyde, F. & Rudloff, B. Set-valued risk measures for conical market models. Math Finan Econ 5, 1–28 (2011). https://doi.org/10.1007/s11579-011-0047-0
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DOI: https://doi.org/10.1007/s11579-011-0047-0
Keywords
- Set-valued risk measures
- Coherent risk measures
- Conical market model
- Legendre–Fenchel transform
- Convex duality
- Transaction costs
- Super-hedging