Risk Measures in the Form of Infimal Convolution

Abstract

The properties of risk measures in the form of infimal convolution are analyzed. The dual representation of such measures, their subdifferential, extremum conditions, representation for optimization and use in constraints are described. The results of the study are demonstrated by examples of known risk measures of such structure. This allows systematization of the available results and facilitates a potential search for new variants of risk measures.

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Correspondence to V. S. Kirilyuk.

Additional information

The study was partially supported by the grant CPEA-LT-2016/10003 of the Norwegian Agency for International Cooperation and Quality Enhancement in Higher Education (Diku).

Translated from Kibernetyka ta Systemnyi Analiz, No. 1, January–February, 2021, pp. 35–54.

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Kirilyuk, V.S. Risk Measures in the Form of Infimal Convolution. Cybern Syst Anal 57, 30–46 (2021). https://doi.org/10.1007/s10559-021-00327-z

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Keywords

  • infimal convolution
  • convex risk measure
  • coherent risk measure
  • conditional value-at-risk
  • dual representation
  • subdifferential
  • expected utility
  • deterministic equivalent