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|Author(s):||Alois Pichler, University of Vienna||Title:||On the Geometry of Acceptability Functionals|
|Date of Acceptance:||28.11.2011|
Stochastic Programming E-Print Series |
|Editors:||Julie L. Higle; Werner Römisch; Surrajeet Sen|
|Complete Preprint:||pdf (urn:nbn:de:kobv:11-100196813)|
|Keywords (eng):||risk measure, continuity properties, Wasserstein and Kantorovich distantce, optimal transport|
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|In this paper we discuss the geometry of acceptability functionals or risk measures. The dependence
of the random variable is investigated ﬁrst. The main contribution and focus of this paper is to study
how acceptability functionals vary whenever the underlying probability measure is perturbed.|
It turns out that the Wasserstein distance provides a valuable notion of distance, and may acceptability functionals allow a precise quantiﬁcation in terms of this distance.
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