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Dual Representation Theorem for Conditional Orlicz Spaces over Random Normed Modules

The dual of the conditional Orlicz heart generated from a random normed module is shown to be the conditional Orlicz space generated from the random conjugate space. Building on a newly defined random Orlicz function and the denseness of the Orlicz heart in the (epsilon,lambda)-topology, this extends classical Orlicz-space duality into the module-over-L0 setting used to model conditional risk measures.

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A DUAL REPRESENTATION THEOREM ON THE CONDITIONAL ORLICZ SPACE GENERATED FROM A RANDOM NORMED MODULE

This paper introduces the notion of a random Orlicz function and, from it, the conditional Orlicz space generated by a random normed module (RN module) - a random-variable-valued generalization of a …