Conditional Interior and Conditional Closure of Random Sets

Meriam El Mansour () and Emmanuel Lépinette ()
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Meriam El Mansour: Paris Dauphine University, PSL Research University
Emmanuel Lépinette: Paris Dauphine University, PSL Research University

Journal of Optimization Theory and Applications, 2020, vol. 187, issue 2, No 3, 356-369

Abstract: Abstract 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.

Keywords: Conditional random set; Conditional optimization; Super-hedging problem; European option; Mathematical finance; 52-02; 60D05; 46N10; 60-02; 54-02; 91-02 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (10)

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DOI: 10.1007/s10957-020-01768-w

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