EconPapers    
Economics at your fingertips  
 

Coherent risk measures, coherent capital allocations and the gradient allocation principle

A. Buch and G. Dorfleitner

Insurance: Mathematics and Economics, 2008, vol. 42, issue 1, 235-242

Abstract: 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.

Date: 2008
References: Add references at CitEc
Citations: View citations in EconPapers (52)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-6687(07)00020-0
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:42:y:2008:i:1:p:235-242

Access Statistics for this article

Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

More articles in Insurance: Mathematics and Economics from Elsevier
Bibliographic data for series maintained by Catherine Liu (repec@elsevier.com).

 
Page updated 2024-12-28
Handle: RePEc:eee:insuma:v:42:y:2008:i:1:p:235-242