MAXIMUM LEBESGUE EXTENSION OF CONVEX RISK MEASURES

Keita Owari
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Keita Owari: Graduate School of Economics, University of Tokyo, Tokyo

No CARF-F-287, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

Abstract: Given a convex risk measure on $L^\infty$ having the Lebesgue property, we construct a solid space of random variables on which the original risk measure is extended preserving the Lebesgue property (on the entire space). This space is an order-continuous Banach lattice, and is maximum among all solid spaces admitting such a regular extension. We then characterize the space in terms of uniform integrability of certain families. As a byproduct, we present a generalization of Jouini-Schachermayer-Touzi’s theorem on the weakcompactness characterization of Lebesgue property, which is valid for any solid vector spaces of random variables, and does not require any topological property of the space.

Pages: 26 pages
Date: 2012-08
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Persistent link: https://EconPapers.repec.org/RePEc:cfi:fseres:cf287

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