Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Next Article Journal of Convex Analysis 09 (2002), No. 1, 237--244Copyright Heldermann Verlag 2002 Convex Stochastic Duality and the "Biting Lemma" Igor V. Evstigneev School of Economic Studies, University of Manchester, Oxford Road, Manchester M13 9PL, Great Britain igor.evstigneev@man.ac.uk Sjur D. Flåm Dept. of Economics, University of Bergen, Fosswickels gate 6, 5007 Bergen, Norway sjur.flaam@econ.uib.no [Abstract-pdf] A standard approach to duality in stochastic optimization problems with constraints in $L_{\infty}$ relies upon the Yosida - Hewitt theorem. We develop an alternative technique which employs only "elementary" means. The technique is based on an $\varepsilon$-regularization of the original problem and on passing to the limit as $\varepsilon \to 0$ with the help of a simple measure-theoretic fact -- the biting lemma. Keywords: Stochastic optimization, convex duality, constraints in L-infinity, stochastic Lagrange multipliers, bounded sets in L-1, biting lemma, Gale's economic model. MSC: 90C15, 51A41; 90C19, 90A16 [ Fulltext-pdf  (262  KB)]