Entropy Coherent and Entropy Convex Measures of Risk - Eurandom

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

Results [2] ◮ It entails that convex, entropy convex and entropy coherent measures of risk induce linear or exponential utility functions in the theories of variational, homothetic and multiple priors preferences. ◮ We show further that, under a normalization condition, this characterization remains valid when the condition of translation invariance is replaced by requiring convexity. ◮ The mathematical details in the proofs of these characterization results are delicate. Entropy Coherent and Entropy Convex Measures of Risk Advances in Financial Mathematics, Eurandom, Eindhoven 14/40
Results [3] ◮ These connections suggest two new subclasses of convex risk measures: entropy coherent and entropy convex measures of risk, and our second contribution is to study their properties. ◮ We show that they satisfy many appealing properties. ◮ We prove various results on the dual conjugate function for entropy coherent and entropy convex measures of risk. We show in particular that, quite exceptionally, the dual conjugate function can explicitly be identified under some technical conditions. ◮ We also study entropy coherent and entropy convex measures of risk under the assumption of distribution invariance. Due to their convex nature, a feature that singles out entropy convex measures of risk in the class of negative certainty equivalents under homothetic preferences, we can obtain explicit representation results in this setting. ◮ Some financial applications and examples of these risk measures are also provided, explicitly utilizing some of the representation results derived. Entropy Coherent and Entropy Convex Measures of Risk Advances in Financial Mathematics, Eurandom, Eindhoven 15/40
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: Results [1] The contribution of thi
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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