Entropy Coherent and Entropy Convex Measures of Risk - Eurandom

5. Distribution Invariant Representation [1]
◮ Let
Ψ = {ψ : [0, 1] → [0, 1]
|ψ is concave, right-continuous at zero with ψ(0+) = 0 and ψ(1) = 1}.
◮ For ψ ∈ Ψ and X ∈ L ∞ we define Eψ [X] :=ÊXdψ(P).
◮ Furthermore, we define
eγ,ψ(X) := γ logEψexp−X
eγ,ψ(P)(X).
γ=:
Entropy Coherent and Entropy Convex Measures of Risk Advances in Financial Mathematics, Eurandom, Eindhoven 35/40