Entropy Coherent and Entropy Convex Measures of Risk - Eurandom

More documents

Recommendations

Info

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

Other Reference Measure In certain situations the agent could consider other reference measures Q ≪ P. Then we define the entropy eγ,Q with respect to Q as eγ,Q(X) = γ logEQexp−X γ. Entropy Coherent and Entropy Convex Measures of Risk Advances in Financial Mathematics, Eurandom, Eindhoven 20/40
Entropy Coherence and Entropy Convexity Definition We call a mapping ρ : L ∞ → R γ-entropy coherent, γ ∈ [0, ∞], if there exists a set M ⊂ Q such that ρ(X) = sup eγ,Q(X). Q∈M It will be interesting to consider as well a more general class of risk measures: Definition The mapping ρ : L ∞ → R is γ-entropy convex, γ ∈ [0, ∞], if there exists a penalty function c : Q → [0, ∞] with infQ∈Q c(Q) = 0, such that ρ(X) = sup {eγ,Q(X) − c(Q)}. Q∈Q Entropy Coherent and Entropy Convex Measures of Risk Advances in Financial Mathematics, Eurandom, Eindhoven 21/40
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 and 16: Results [3] ◮ These connections s
Page 17 and 18: 2. Entropic Measures of Risk [1] We
Page 19: Two Interpretations 1. Kullback-Lei
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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?