Sure wins, separating probabilities and the representation of linear functionals

Cassese, Gianluca

doi:10.1016/j.jmaa.2009.01.013

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Journal article

Sure wins, separating probabilities and the representation of linear functionals

Cassese, Gianluca Istituto di finanza (IFin), Facoltà di scienze economiche, Università della Svizzera italiana, Svizzera

2009

Published in:

Journal of mathematical analysis and applications. - Elsevier. - 2009, vol. 354, no. 2, p. 558-563

finitely additive supermartingales

integral representation of linear functionals

English We discuss conditions under which a convex cone K ⊂ RΩ admits a finitely additive probability m such that supk∈K m(k) ≤ 0. Based on these, we characterize those linear functionals that are representable as finitely additive expectations. A version of Riesz decomposition based on this property is obtained as well as a characterisation of positive functionals on the space of integrable functions.

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