The relations among the three kinds of conditional risk measures

DOI10.1007/S11425-014-4840-0zbMath1316.46004OpenAlexW1973114228MaRDI QIDQ477159

Shien Zhao, Xiao Lin Zeng, Tie-Xin Guo

Publication date: 2 December 2014

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-014-4840-0

zbMATH Keywords

extensionrandom normed module\(L^{\infty}({\mathcal E})\)-conditional risk measure\(L^{p}_{{\mathcal F}}({\mathcal E})\)-conditional risk measure\(L^{p}({\mathcal E})\)-conditional risk measure (\(1\leq p< +\infty\))countable concatenation property

Mathematics Subject Classification ID

Stochastic models in economics (91B70) Utility theory (91B16) Theorems of Hahn-Banach type; extension and lifting of functionals and operators (46A22) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25) Reflexivity and semi-reflexivity (46A25)

Related Items (12)

\(L^0\)-convex compactness and random normal structure in \(L^0(\mathcal{F}, B)\) ⋮ On \(L^0\)-convex compactness in random locally convex modules ⋮ Stability in locally \(L^{0}\)-convex modules and a conditional version of James' compactness theorem ⋮ A characterization for a complete random normed module to be mean ergodic ⋮ Some results on random smoothness ⋮ Unnamed Item ⋮ Randomized versions of Mazur lemma and Krein-Smulian theorem ⋮ Two fixed point theorems in complete random normed modules and their applications to backward stochastic equations ⋮ The fundamental theorem of affine geometry in regular \(L^0\)-modules ⋮ L⁰-convex compactness and its applications to random convex optimization and random variational inequalities ⋮ Semigroups of continuous module homomorphisms on complex complete random normed modules ⋮ Clarke's fixed point theorem on a complete random normed module

Cites Work

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• Random duality
• A duality theorem for a convex programming problem in order complete vector lattices
• Extension theorems of continuous random linear operators on random domains
• Conditional and dynamic convex risk measures
• Coherent Measures of Risk
• Approaches to Conditional Risk
• Stochastic finance. An introduction in discrete time

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