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Positivity - There is an error in Proposition 3.10. In fact, the stated proof only shows 相似文献
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Recently Heyde, Kou and Peng [C.C. Heyde, S.G. Kou, X.H. Peng, What is a good external risk measure: Bridging the gaps between robustness, subadditivity, and insurance risk measures, 2007, preprint.] proposed the notion of a natural risk statistic associated with a finite sample that relaxes the subadditivity assumption in the classical coherent risk statistics. In this note we use convex analysis to provide alternate proofs of the representation results regarding natural risk statistics. 相似文献
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We provide a characterization in terms of Fatou closedness for weakly closed monotone convex sets in the space of \({\mathcal P}\)-quasisure bounded random variables, where \({\mathcal P}\) is a (possibly non-dominated) class of probability measures. Applications of our results lie within robust versions the Fundamental Theorem of Asset Pricing or dual representation of convex risk measures. 相似文献
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Gregor Svindland 《Mathematics and Financial Economics》2010,3(1):39-43
We study continuity properties of law-invariant (quasi-)convex functions \({f:L^\infty(\Omega, \mathcal{F}, \mathbb{P}) \to (-\infty,\infty]}\) over a non-atomic probability space \({(\Omega, \mathcal{F}, \mathbb{P})}\). This is a supplementary note to Jouini et al. (Adv Math Econ 9:49–71, 2006). 相似文献
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Hannes Hoffmann Thilo Meyer-Brandis Gregor Svindland 《Mathematics and Financial Economics》2018,12(3):413-444
We consider families of strongly consistent multivariate conditional risk measures. We show that under strong consistency these families admit a decomposition into a conditional aggregation function and a univariate conditional risk measure as introduced Hoffmann et al. (Stoch Process Appl 126(7):2014–2037, 2016). Further, in analogy to the univariate case in Föllmer (Stat Risk Model 31(1):79–103, 2014), we prove that under law-invariance strong consistency implies that multivariate conditional risk measures are necessarily multivariate conditional certainty equivalents. 相似文献
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Gregor Svindland 《Mathematics and Financial Economics》2014,8(3):241-247
We study, for functions and sets, the relation between law invariance, preserving the convex or uniform order, and dilatation monotonicity based on duality arguments. 相似文献
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