Entropy Coherent and Entropy Convex Measures of Risk - Eurandom

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$Continuous-time random walks, fractional calculus and ... - Eurandom$

Multiple Priors Preferences vs. Convex Measures of Risk ◮ Compare to mX = φ −1sup EQ [φ(−X)], Q∈M⊂Q ρ(X) = sup {EQ [−X] − α(Q)}. Q∈Q ◮ Question: find sufficient and necessary conditions. Entropy Coherent and Entropy Convex Measures of Risk Advances in Financial Mathematics, Eurandom, Eindhoven 10/40
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
Page 1 and 2: Entropy Coherent and Entropy Convex
Page 3 and 4: Convex Measures of Risk ◮ Convex
Page 5 and 6: Multiple Priors Preferences ◮ A s
Page 7 and 8: Homothetic Preferences ◮ Recently
Page 9: Variational and Homothetic Preferen
Page 13 and 14: Results [1] The contribution of thi
Page 15 and 16: Results [3] ◮ These connections s
Page 17 and 18: 2. Entropic Measures of Risk [1] We
Page 19 and 20: Two Interpretations 1. Kullback-Lei
Page 21 and 22: Entropy Coherence and Entropy Conve
Page 23 and 24: Again Two Interpretations [2] The e
Page 25 and 26: A Basic Duality Result Define and T
Page 27 and 28: 3. Characterization Results [1] Rec
Page 29 and 30: Remark 1 ◮ The case that ρ is en
Page 31 and 32: Characterization Results [3] Recall
Page 33 and 34: 4. Duality Results [1] Recall that
Page 35 and 36: 5. Distribution Invariant Represent
Page 37 and 38: 6.1 Risk Sharing ◮ Suppose that t
Page 39 and 40: Portfolio Optimization and Indiffer

Entropy Coherent and Entropy Convex Measures of Risk - Eurandom

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