Quotation Feinstein, Zachary, Rudloff, Birgit. 2017. A recursive algorithm for multivariate risk measures and a set-valued Bellman's principle. Journal of Global Optimization 68 (1), 47-69.




A method for calculating multi-portfolio time consistent multivariate risk measures in discrete time is presented. Market models for d assets with transaction costs or illiquidity and possible trading constraints are considered on a finite probability space. The set of capital requirements at each time and state is calculated recursively backwards in time along the event tree. We motivate why the proposed procedure can be seen as a set-valued Bellman’s principle, that might be of independent interest within the growing field of set optimization. We give conditions under which the backwards calculation of the sets reduces to solving a sequence of linear, respectively convex vector optimization problems. Numerical examples are given and include superhedging under illiquidity, the set-valued entropic risk measure, and the multi-portfolio time consistent version of the relaxed worst case risk measure and of the set-valued average value at risk.


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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Journal article
Journal Journal of Global Optimization
Citation Index SCI
WU-Journal-Rating new FIN-A
Language English
Title A recursive algorithm for multivariate risk measures and a set-valued Bellman's principle
Volume 68
Number 1
Year 2017
Page from 47
Page to 69
Reviewed? Y
URL http://arxiv.org/pdf/1508.02367.pdf
DOI http://dx.doi.org/10.1007/s10898-016-0459-8


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