Maximum Lebesgue Extension of Monotone Convex Functions

Keita Owari
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Keita Owari: The University of Tokyo

No CARF-F-315, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

Abstract: 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 Orlicztype 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.

Pages: 33 pages
Date: 2013-05
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Related works:
Working Paper: Maximum Lebesgue Extension of Monotone Convex Functions (2014)
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