A supermartingale relation for multivariate risk measures. Issue 12 (2nd December 2018)

• Record Type: Journal Article
• Authors: Feinstein, Zachary; Rudloff, Birgit
• Is Part Of: Quantitative finance. Volume 18:Issue 12(2018)
• Page Start: 1971
• Page End: 1990
• Publication Date: 2018-12-02
• Subjects: Set-valued supermartingale -- Time consistency -- Dynamic risk measures -- Transaction costs -- Set-valued risk measures -- Multivariate risks; 91B30 -- 26E25 -- 60G48 -- C61 -- G15 -- G18 -- G28 -- G32; Finance -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Investments -- Mathematics -- Periodicals; Economics -- Periodicals; Finances -- Modèles mathématiques -- Périodiques; 332.015118
• DOI: 10.1080/14697688.2018.1459810
• Languages: English
• ISSNs: 1469-7688

Abstract

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.