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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/86052 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/86052 http://eprints.org/relation/issmallThumbnailVersionOf https://pure.iiasa.ac.at/id/document/86052 archive 353 disk0/00/01/56/59 2019-01-07 09:03:44 2021-08-27 17:31:14 2019-01-07 09:03:44 article show Escobar D.D. Pflug G. 1361 0000-0001-8215-3550 pub prog_risk Ambiguity; Distortion premium; Dual representation; Premium principles; Risk measures; Wasserstein distance Distortion (Denneberg in ASTIN Bull 20(2):181–190, 1990) is a well known premium calculation principle for insurance contracts. In this paper, we study sensitivity properties of distortion functionals w.r.t. the assumptions for risk aversion as well as robustness w.r.t. ambiguity of the loss distribution. Ambiguity is measured by the Wasserstein distance. We study variances of distances for probability models and identify some worst case distributions. In addition to the direct problem we also investigate the inverse problem, that is how to identify the distortion density on the basis of observations of insurance premia. 2020 published Springer 10.1007/s10479-018-3119-1 229 public Annals of Operations Research 292 771-794 TRUE 1572-9338 FALSE no info:eu-repo/semantics/article