Entropy Coherent and Entropy Convex Measures of Risk - Eurandom

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Outline 1. Introduction 2. Entropic Measures of Risk 3. Characterization Results 4. Duality Results 5. Distribution Invariant Representation 6. Applications and Examples 7. Conclusions Entropy Coherent and Entropy Convex Measures of Risk Advances in Financial Mathematics, Eurandom, Eindhoven 16/40
2. Entropic Measures of Risk [1] We fix a probability space (Ω, F, P) and fix a scalar γ ∈ [0, ∞]. Let X ∈ L ∞ . Define eγ(X) := γ logEexp− X γ. ◮ Entropic measures of risk (exponential premiums) emerge in various paradigms. Entropy Coherent and Entropy Convex Measures of Risk Advances in Financial Mathematics, Eurandom, Eindhoven 17/40
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 and 10: Variational and Homothetic Preferen
Page 11 and 12: Question Rephrased [1] ◮ In other
Page 13 and 14: Results [1] The contribution of thi
Page 15: Results [3] ◮ These connections s
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

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