Closedness of convex sets in Orlicz spaces with applications to dual representation of risk measures

DOI10.4064/sm180404-3-1zbMath1445.46032arXiv1610.08806OpenAlexW3122766989WikidataQ127734878 ScholiaQ127734878MaRDI QIDQ5237161

Niushan Gao, Denny H. Leung, Foivos Xanthos

Publication date: 16 October 2019

Published in: Studia Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.08806

zbMATH Keywords

Banach latticesOrlicz spacesrisk measuresOrlicz heartsorder closuresorder closed setssequentially closed setsKrein-\(\check{}\) smulian property

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Duality theory for topological vector spaces (46A20)

Related Items

Dual representations for systemic risk measures based on acceptance sets, Automatic Fatou property of law-invariant risk measures, The order-type Banach-Saks properties, Mean‐ portfolio selection and ‐arbitrage for coherent risk measures, Smallest order closed sublattices and option spanning, On closedness of convex sets in Banach lattices, Fatou property, representations, and extensions of law-invariant risk measures on general Orlicz spaces, \(um\)-topology in multi-normed vector lattices, The strong Fatou property of risk measures, On closedness of law-invariant convex sets in rearrangement invariant spaces, Surplus-Invariant Risk Measures, Convex functions on dual Orlicz spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Functional analysis, Sobolev spaces and partial differential equations
• Duality for unbounded order convergence and applications
• Fatou property, representations, and extensions of law-invariant risk measures on general Orlicz spaces
• Convex functions on dual Orlicz spaces
• Maximum Lebesgue extension of monotone convex functions
• Coherent Measures of Risk
• RISK MEASURES ON ORLICZ HEARTS
• On the C‐property and ‐representations of risk measures
• Biorthogonal systems in Banach spaces
• Stochastic finance. An introduction in discrete time
• Stopping Times and Directed Processes