Entropy Coherent and Entropy Convex Measures of Risk - Eurandom

Question Rephrased [1]
◮ In other words, we consider
with
ρ(X) = φ −1 (¯ρ(−φ(−X))),
¯ρ(X) = sup
Q∈M⊂Q
EQ [−X] .
◮ Preferences of Gilboa and Schmeidler (1989).
◮ We also consider
with
ρ(X) = φ −1 (¯ρ(−φ(−X))),
¯ρ(X) = sup {EQ [−X] − α(Q)}.
Q∈Q
◮ Preferences of Maccheroni, Marinacci and Rustichini (2006).
◮ In the latter case, negative certainty equivalents are invariant under
translation of u (or φ).
◮ Traditionally (in the models of Savage, 1954, and Gilboa and Schmeidler,
1989), negative certainty equivalents are invariant under both translation
and positive multiplication of u (or φ).
Entropy Coherent and Entropy Convex Measures of Risk Advances in Financial Mathematics, Eurandom, Eindhoven 11/40