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A Supermartingale Relation for Multivariate Risk Measures

Author(s): Feinstein, Zachary; Rudloff, Birgit

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Abstract: The equivalence between multiportfolio time consistency of a dynamic multivariate risk measure and a supermartingale property is proven. Furthermore, the dual variables under which this set-valued supermartingale is a martingale are characterized as the worst-case dual variables in the dual representation of the risk measure. Examples of multivariate risk measures satisfying the supermartingale property are given. Crucial for obtaining the results are dual representations of scalarizations of set-valued dynamic risk measures, which are of independent interest in the fast growing literature on multivariate risks.
Publication Date: 8-Jun-2018
Citation: Feinstein, Z. & B. Rudloff (2018). A supermartingale relation for multivariate risk measures. Quantitative Finance, 18:12, 1971-1990, doi:10.1080/14697688.2018.1459810
DOI: doi:10.1080/14697688.2018.1459810
Pages: 1971 - 1990
Type of Material: Journal Article
Journal/Proceeding Title: Quantitative Finance
Version: Author's manuscript

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