Entropy Coherent and Entropy Convex Measures of Risk - Eurandom

Entropy Coherence and Entropy Convexity
Definition
We call a mapping ρ : L ∞ → R γ-entropy coherent, γ ∈ [0, ∞], if there exists a
set M ⊂ Q such that
ρ(X) = sup eγ,Q(X).
Q∈M
It will be interesting to consider as well a more general class of risk measures:
Definition
The mapping ρ : L ∞ → R is γ-entropy convex, γ ∈ [0, ∞], if there exists a
penalty function c : Q → [0, ∞] with infQ∈Q c(Q) = 0, such that
ρ(X) = sup {eγ,Q(X) − c(Q)}.
Q∈Q
Entropy Coherent and Entropy Convex Measures of Risk Advances in Financial Mathematics, Eurandom, Eindhoven 21/40