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Kusuoka Representations of Coherent Risk Measures in General Probability Spaces
Company: Optimization Online
Company Url: Click here to open
Year Of Publication: 2013
Month Of Publication: May
Resource Link: Click here to open
Pages: 16
Download Count: 0
View Count: 1585
Comment Num: 0
Language: English
Source: working paper
Who Can Read: Free
Date: 8-12-2014
Publisher: Administrator
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
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Noyan, Nilay Sign in to follow this author
Rudolf, Gabor Sign in to follow this author
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