2013/04/30 by Keita Owari
Mathematics · Economics, Econometrics and Finance · #math.FA #math.PR #q-fin.RM
paper · pdf · doi:10.1016/j.jfa.2014.01.002
published as Journal of Functional Analysis, 266, issue 6, 2014, pp. 3572-3611 · To Appear in Journal of Functional Analysis, 32 pages
arxiv created 2014/01/19 · arxiv updated 2014/02/20
Given a monotone convex function on the space of essentially bounded random variables with the Lebesgue property (order continuity), we consider its extension preserving the Lebesgue property to as big solid vector space of random variables as possible. We show that there exists a maximum such extension, with explicit construction, where the maximum domain of extension is obtained as a (possibly proper) subspace of a natural Orlicz-type space, characterized by a certain uniform integrability property. As an application, we provide a characterization of the Lebesgue property of monotone convex function on arbitrary solid spaces of random variables in terms of uniform integrability and a "nice" dual representation of the function.