Buch, A. and Dorfleitner, G. (2008) Coherent risk measures, coherent capital allocations and the gradient allocation principle. INSURANCE MATHEMATICS & ECONOMICS, 42 (1). pp. 235-242. ISSN 0167-6687,
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The gradient allocation principle, which generalizes the most popular specific allocation principles, is commonly proposed in the literature as a means of distributing a financial institution's risk capital to its constituents. This paper is concerned with the axioms defining the coherence of risk measures and capital allocations, and establishes results linking the two coherence concepts in the context of the gradient allocation principle. The following axiom pairs are shown to be equivalent: positive homogeneity and full allocation, subadditivity and "no undercut", and translation invariance and riskless allocation. Furthermore, we point out that the symmetry property holds if and only if the risk measure is linear. As a consequence, the gradient allocation principle associated with a coherent risk measure has the properties of full allocation and "no undercut", but not symmetry unless the risk measure is linear. The results of this paper are applied to the covariance, the semi-covariance, and the expected shortfall principle. We find that the gradient allocation principle associated with a nonlinear risk measure can be coherent, in a suitably restricted setting. (C) 2007 Elsevier B.V. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | EXPECTED SHORTFALL; risk capital allocation; gradient allocation principle; coherent risk measures; coherent capital allocations |
| Subjects: | 600 Technology > 650 Management & auxiliary services |
| Divisions: | Business, Economics and Information Systems > Institut für Betriebswirtschaftslehre > Lehrstuhl für Finanzierung (Prof. Dr. Gregor Dorfleitner) |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 09 Nov 2020 13:26 |
| Last Modified: | 09 Nov 2020 13:26 |
| URI: | https://pred.uni-regensburg.de/id/eprint/31420 |
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