Conditional Interior and Conditional Closure of Random Sets

In this paper, we introduce two new types of conditional random set taking values in a Banach space: the conditional interior and the conditional closure. The conditional interior is a version of the conditional core, as introduced by A. Truffert and recently developed by Lépinette and Molchanov, an...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2020-11, Vol.187 (2), p.356-369
Main Authors: El Mansour, Meriam, Lépinette, Emmanuel
Format: Article
Language:English
Subjects:
Applications of Mathematics
Banach spaces
Calculus of Variations and Optimal Control
Optimization
Closures
Engineering
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Probability
Random variables
Theory of Computation
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Summary:In this paper, we introduce two new types of conditional random set taking values in a Banach space: the conditional interior and the conditional closure. The conditional interior is a version of the conditional core, as introduced by A. Truffert and recently developed by Lépinette and Molchanov, and may be seen as a measurable version of the topological interior. The conditional closure is a generalization of the notion of conditional support of a random variable. These concepts are useful for applications in mathematical finance and conditional optimization.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-020-01768-w