Quotation Feinstein, Zachary, Rudloff, Birgit. 2021. Time consistency for scalar multivariate risk measures. Statistics and Risk Modeling. 38 (3-4), 71-90.




In this paper we present results on dynamic multivariate scalar risk measures, which arise in markets with transaction costs and systemic risk. Dual representations of such risk measures are presented. These are then used to obtain the main results of this paper on time consistency; namely, an equivalent recursive formulation of multivariate scalar risk measures to multiportfolio time consistency. We are motivated to study time consistency of multivariate scalar risk measures as the superhedging risk measure in markets with transaction costs (with a single eligible asset) does not satisfy the usual scalar concept of time consistency. In fact, scalar risk measures with the same scalarization weight at all times would not be time consistent in general. The deduced recursive relation for the scalarizations of multiportfolio time consistent set-valued risk measures provided in this paper requires consideration of the entire family of scalarizations. In this way we develop a direct notion of a “moving scalarization” for scalar time consistency that corroborates recent research on scalarizations of dynamic multi-objective problems.


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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Journal article
Journal Statistics and Risk Modeling
WU-Journal-Rating new FIN-A, VW-C
Language English
Title Time consistency for scalar multivariate risk measures
Volume 38
Number 3-4
Year 2021
Page from 71
Page to 90
Reviewed? Y
DOI https://doi.org/10.1515/strm-2019-0023
Open Access N


Rudloff, Birgit (Details)
Feinstein, Zachary (Washington University in St. Louis, United States/USA)
Institute for Statistics and Mathematics IN (Details)
Research areas (ÖSTAT Classification 'Statistik Austria')
1118 Probability theory (Details)
1137 Financial mathematics (Details)
5361 Financial management (Details)
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