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Volume 57 >>> № 1 JANUARY — FEBRUARY 2021

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UDC 519.21

V.S. Kirilyuk¹

¹ V.M. Glushkov Institute of Cybernetics, National Academy
of Sciences of Ukraine, Kyiv, Ukraine

RISK MEASURES IN THE FORM OF INFIMAL CONVOLUTION

Abstract. The properties of risk measures in the form of infimal convolution are studied. 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 construction. This allows systematization of the well-known results and facilitates a potential search for new variants of risk measures.

Keywords: infimal convolution, convex risk measure, coherent risk measure, conditional value-at-risk, dual representation, subdifferential, expected utility, deterministic equivalent.

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