Maximum Lebesgue Extension Of Convex Risk Measures
AbstractGiven 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-Touziâ€™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.
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Bibliographic InfoPaper provided by Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo in its series CARF F-Series with number CARF-F-287.
Length: 26 pages
Date of creation: Aug 2012
Date of revision:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-09-09 (All new papers)
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