Nonlinear expectations of random sets

DOI10.1007/s00780-020-00442-3zbMath1461.91283arXiv1903.04901OpenAlexW3123109610MaRDI QIDQ2022754

Anja Mühlemann, Ilya S. Molchanov

Publication date: 29 April 2021

Published in: Finance and Stochastics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.04901

zbMATH Keywords

utilitytransaction costsset-valued functionrandom setsublinear expectationselection expectationmultiasset portfoliosuperlinear expectation

Mathematics Subject Classification ID

Set-valued set functions and measures; integration of set-valued functions; measurable selections (28B20) Utility theory (91B16) Portfolio theory (91G10)

Related Items (3)

Convex bodies generated by sublinear expectations of random vectors ⋮ Depth and outliers for samples of sets and random sets distributions ⋮ Set-valued risk measures as backward stochastic difference inclusions and equations

Cites Work

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• Complete duality for quasiconvex and convex set-valued functions
• Multivariate dispersion, central regions and depth. The lift zonoid approach
• A duality theory for set-valued functions. I: Fenchel conjugation theory
• Markets with transaction costs. Mathematical theory.
• Multivariate risks and depth-trimmed regions
• On convex risk measures on \(L^{p}\)-spaces
• Scalar convergence of convex sets
• A strong law of large numbers for random compact sets
• Integrals, conditional expectations, and martingales of multivalued functions
• Lift expectations of random sets
• General notions of statistical depth function.
• Set-valued risk measures for conical market models
• Asset pricing theory for two price economies
• Risk arbitrage and hedging to acceptability under transaction costs
• Conditional cores and conditional convex hulls of random sets
• A characterization theorem for Aumann integrals
• Integrals of set-valued functions
• MULTIVARIATE RISK MEASURES: A CONSTRUCTIVE APPROACH BASED ON SELECTIONS
• Duality for Set-Valued Measures of Risk
• Hedging of Claims with Physical Delivery under Convex Transaction Costs
• Integral Representation Without Additivity
• Random Sets in Econometrics
• Theory of Random Sets
• Nonlinear Expectations and Stochastic Calculus under Uncertainty
• Set-valued Optimization
• Convex Bodies The Brunn-MinkowskiTheory
• Stochastic finance. An introduction in discrete time

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