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Kusuoka representations of coherent risk measures in general probability spaces

Noyan, Nilay and Rudolf, Gabor (2015) Kusuoka representations of coherent risk measures in general probability spaces. Annals of Operations Research, 229 (1). pp. 591-605. ISSN 0254-5330 (Print) 1572-9338 (Online)

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Official URL: http://dx.doi.org/10.1007/s10479-014-1748-6

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.

Item Type:Article
Uncontrolled Keywords:Kusuoka representation· Coherent risk measures· Spectral risk measures· Acceptability functional· Law invariance· Comonotonicity
Subjects:Q Science > Q Science (General)
ID Code:25340
Deposited By:Nilay Noyan
Deposited On:23 Dec 2014 14:43
Last Modified:17 Dec 2015 10:26

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