A supermartingale relation for multivariate risk measures

Zachary Feinstein, Birgit Rudloff

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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.

Original languageEnglish
Pages (from-to)1971-1990
Number of pages20
JournalQuantitative Finance
Volume18
Issue number12
DOIs
StatePublished - 2 Dec 2018

Keywords

  • Dynamic risk measures
  • Multivariate risks
  • Set-valued risk measures
  • Set-valued supermartingale
  • Time consistency
  • Transaction costs

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