Conditional supremum in Riesz spaces and applications

We extend the concept of conditional supremum to the measure-free setting of Riesz spaces via the conditional expectation operator. We explore its properties and show how this tool is crucial in generalizing various results across multiple disciplines to the framework of Riesz spaces. Among other applications, we utilize this concept in finance to derive characterizations of certain financial conditions.(c) 2023 Elsevier Inc. All rights reserved.

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In this paper, we extend the concept of conditional supremum to the measure-free setting of Riesz spaces using the conditional expectation operator. We explore its properties and highlight its crucial role in generalizing results from various disciplines to the framework of Riesz spaces. We also demonstrate its application in finance for characterizing certain financial conditions.