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On Two Approaches to Coherent Risk Contribution

15 Pages Posted: 20 May 2011  

Alexander S. Cherny

Moscow State University

Dmitri Orlov

affiliation not provided to SSRN

Date Written: July 2011

Abstract

We compare two approaches to the coherent risk contribution: the directional risk contribution is defined as where ρ is a coherent risk measure; the linear risk contribution ρl (X; Y) is defined through a set of axioms, one of which is the linearity in X. The linear risk contribution exists and is unique for any ρ from the Weighted V@R class. We provide the representation for both risk contributions in the general setting as well as in some examples, including the MINV@R risk measure defined as where X1, . . . , XN are independent copies of X.

Keywords: conditional V@R, coherent risk measure, directional risk contribution, linear risk contribution, minimal extreme measure, MINV@R, Weighted V@R

Suggested Citation

Cherny, Alexander S. and Orlov, Dmitri, On Two Approaches to Coherent Risk Contribution (July 2011). Mathematical Finance, Vol. 21, Issue 3, pp. 557-571, 2011. Available at SSRN: https://ssrn.com/abstract=1841237 or http://dx.doi.org/10.1111/j.1467-9965.2010.00441.x

Alexander S. Cherny (Contact Author)

Moscow State University ( email )

Faculty of Mechanics and Mathematics
Department of Probability Theory
Moscow, 119992
Russia
007 095 939 14 03 (Phone)
007 095 939 14 03 (Fax)

HOME PAGE: http://mech.math.msu.su/~cherny

Dmitri Orlov

affiliation not provided to SSRN

No Address Available

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