Coherent risk measure

Mar 29, 2016

statistics

A coherent risk measure satifies the following features:

sub-additivity: ρ(R₁ + R₂) ≤ ρ(R₁) + ρ(R₂)
monotonicity: ρ(R₁) ≥ ρ(R₂) if R₁ ≥ R₂
positive homogeneity: βρ(R) = ρ(βR), for all β>0.
translation invariant: ρ(R) + c = ρ(c + R) for all constants c.

Beware! the VAR measure violates the first feature (sub-additivity).