Kusuoka representations of coherent risk measures in general probability spaces

Nilay Noyan () and Gábor Rudolf ()

Annals of Operations Research, 2015, vol. 229, issue 1, 605 pages

Abstract: Kusuoka representations provide an important and useful characterization of law invariant coherent risk measures in atomless probability spaces. However, the applicability of these results is limited by the fact that such representations do not always exist in probability spaces with atoms, such as finite probability spaces. We introduce the class of functionally coherent risk measures, which allow us to use Kusuoka representations in any probability space. We show that this class contains every law invariant risk measure that can be coherently extended to a family containing all finite discrete distributions. Thus, it is possible to preserve the desirable properties of law invariant coherent risk measures on atomless spaces without sacrificing generality. We also specialize our results to risk measures on finite probability spaces, and prove a denseness result about the family of risk measures with finite Kusuoka representations. Copyright Springer Science+Business Media New York 2015

Keywords: Kusuoka representation; Coherent risk measures; Spectral risk measures; Acceptability functional; Law invariance; Comonotonicity (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10479-014-1748-6

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