The distortion principle for insurance pricing: properties, identification and robustness

Debora Daniela Escobar () and Georg Ch. Pflug ()
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Debora Daniela Escobar: University of Vienna
Georg Ch. Pflug: ISOR and International Institute for Applied Systems Analysis (IIASA)

Annals of Operations Research, 2020, vol. 292, issue 2, No 10, 794 pages

Abstract: Abstract 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.

Keywords: Ambiguity; Distortion premium; Dual representation; Premium principles; Risk measures; Wasserstein distance (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10479-018-3119-1

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