On conditional Lebesgue property for conditional risk measures

José Orihuela, José Miguel Zapata

Published 2015-09-23Version 1

In this paper we first carry out a study of the connection between the notion of locally $L^0$-convex modules, the analytic basis of the conditional risk measures, and the notion of conditional locally convex spaces. Second, we provide a conditional version of the classical James' Theorem of characterization of weak compactness. Finally, as application of the developed theory we stablish a version of the so-known Jouini-Schachermayer-Touzi Theorem for robust representation of conditional $L^0$-convex risk measures defined on a $L^\infty$-type module with the conditional Lebesgue property.