ON TWO APPROACHES TO COHERENT RISK CONTRIBUTION

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 ρ^l(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, … , X_N are independent copies of X .