On Two Approaches to Coherent Risk Contribution
15 Pages Posted: 20 May 2011
Date Written: July 2011
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
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