## Kusuoka representations of coherent risk measures in general probability spacesNoyan, Nilay and Rudolf, Gabor (2015)
Official URL: http://dx.doi.org/10.1007/s10479-014-1748-6 ## AbstractKusuoka 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.
## Available Versions of this Item- Representations of coherent risk measures in general probability spaces. (deposited 15 Jan 2014 22:01)
- Kusuoka representations of coherent risk measures in general probability spaces. (deposited 23 Dec 2014 14:43)
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- Kusuoka representations of coherent risk measures in general probability spaces. (deposited 23 Dec 2014 14:43)
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