Quotation Ararat, Çagin, Hamel, Andreas, Rudloff, Birgit. 2017. Set-valued shortfall and divergence risk measures. International Journal of Theoretical and Applied Finance 20 (5), 1750026




Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set minimization problems. The dual relationship between these two classes of multivariate risk measures is constructed via a recent Lagrange duality for set optimization. In particular, it is shown that a shortfall risk measure can be written as an intersection over a family of divergence risk measures indexed by a scalarization parameter. Examples include set-valued versions of the entropic risk measure and the average value at risk. As a second step, the minimization of these risk measures subject to trading opportunities is studied in a general convex market in discrete time. The optimal value of the minimization problem, called the market risk measure, is also a set-valued risk measure. A dual representation for the market risk measure that decomposes the effects of the original risk measure and the frictions of the market is proved. Read More: http://www.worldscientific.com/doi/abs/10.1142/S0219024917500261


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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Journal article
Journal International Journal of Theoretical and Applied Finance
WU Journalrating 2009 A
WU-Journal-Rating new FIN-A, STRAT-B, WH-B
Language English
Title Set-valued shortfall and divergence risk measures
Volume 20
Number 5
Year 2017
Page from 1750026
Reviewed? Y
URL http://arxiv.org/pdf/1405.4905.pdf
DOI http://dx.doi.org/10.1142/S0219024917500261


Rudloff, Birgit (Details)
Ararat, Çagin (Bilkent University, Turkey)
Hamel, Andreas (Free University of Bolzano, Italy)
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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