Entropy Coherent and Entropy Convex Measures of Risk - Eurandom

Subdifferential
◮ We define the subdifferential of ρ by
∂ρ(X) = {Q ∈ Q|ρ(X) = EQ [−X] − α(Q)}.
We say that ρ is subdifferentiable if for every X ∈ L ∞ we have ∂ρ(X) = ∅.
◮ For a γ-entropy convex function ρ we define by
∂entropyρ(X) = {Q ∗ ∈ Q|ρ(X) = eγ,Q ∗(X) − c(Q ∗ )}
the entropy subdifferential. Furthermore, if for every X ∈ L ∞ ,
∂entropyρ(X) = ∅, then we say that ρ is entropy subdifferentiable.
Entropy Coherent and Entropy Convex Measures of Risk Advances in Financial Mathematics, Eurandom, Eindhoven 26/40