Conditional expectation for monotone measures, the discrete case

DOI10.1016/S0304-4068(02)00011-3zbMath1013.28015MaRDI QIDQ1850146

Dieter Denneberg

Publication date: 2 December 2002

Published in: Journal of Mathematical Economics (Search for Journal in Brave)

zbMATH Keywords

conditional expectationChoquet integralnon-additive measuresbelief functionsmonotone measureproduct measureChoquet capacities

Mathematics Subject Classification ID

Decision theory (91B06) Contents, measures, outer measures, capacities (28A12) Fuzzy measure theory (28E10)

Related Items (12)

Updating Choquet beliefs ⋮ Products of non-additive measures: a Fubini-like theorem ⋮ Max-min (\(\sigma\)-)additive representation of monotone measures ⋮ Dynamic bid-ask pricing under Dempster-Shafer uncertainty ⋮ Risk capital allocation and cooperative pricing of insurance liabilities. ⋮ Coherent updating of non-additive measures ⋮ On the \(f\)-divergence for discrete non-additive measures ⋮ Dynamic capital allocation with distortion risk measures ⋮ Atoms of monotone set-valued measures and integrals ⋮ Convergence theorems for monotone measures ⋮ Agreeable bets with multiple priors ⋮ A philosophical foundation of non-additive measure and probability

Cites Work

• Maxmin expected utility with non-unique prior
• Towards a frequentist theory of upper and lower probability
• Fuzzy sets as a basis for a theory of possibility
• Distributive lattices and products of capacities
• The product of capacities and belief functions
• Non-additive measure and integral
• Conditioning (updating) non-additive measures
• Max-min (\(\sigma\)-)additive representation of monotone measures
• Cores of cooperative games, superdifferentials of functions, and the Minkowski difference of sets
• Totally monotone core and products of monotone measures
• Interaction transform of set functions over a finite set
• Choquet rationality
• Bayesian updating and belief functions
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