TY - JOUR
T1 - A supermartingale relation for multivariate risk measures
AU - Feinstein, Zachary
AU - Rudloff, Birgit
N1 - Publisher Copyright:
© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2018/12/2
Y1 - 2018/12/2
N2 - 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.
AB - 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.
KW - Dynamic risk measures
KW - Multivariate risks
KW - Set-valued risk measures
KW - Set-valued supermartingale
KW - Time consistency
KW - Transaction costs
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U2 - 10.1080/14697688.2018.1459810
DO - 10.1080/14697688.2018.1459810
M3 - Article
AN - SCOPUS:85048163994
SN - 1469-7688
VL - 18
SP - 1971
EP - 1990
JO - Quantitative Finance
JF - Quantitative Finance
IS - 12
ER -