Multi-asset risk measures
AbstractWe study risk measures for financial positions in a multi-asset setting, representing the minimum amount of capital to raise and invest in eligible portfolios of traded assets in order to meet a prescribed acceptability constraint. We investigate finiteness and continuity properties of these multi-asset risk measures, highlighting the interplay between the acceptance set and the class of eligible portfolios. We develop a new approach to dual representations of convex multi-asset risk measures which relies on a characterization of the structure of closed convex acceptance sets. To avoid degenerate cases we need to ensure the existence of extensions of the underlying pricing functional which belong to the effective domain of the support function of the chosen acceptance set. We provide a characterization of when such extensions exist. Finally, we discuss applications to conical market models and set-valued risk measures, optimal risk sharing, and superhedging with shortfall risk.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1308.3331.
Date of creation: Aug 2013
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-08-23 (All new papers)
- NEP-RMG-2013-08-23 (Risk Management)
- NEP-UPT-2013-08-23 (Utility Models & Prospect Theory)
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