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Conditional interior and conditional closure of a random set

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Conditional_interior_and_the_conditional_closure_of_a_random_sets.pdf (244.3Kb)
Date
2019-08
Publisher city
Paris
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Publishing date
2019
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-02272243
Dewey
Probabilités et mathématiques appliquées
Sujet
random optimization; conditional closure; conditional interior; Random set; conditional core; mathematical finance
URI
https://basepub.dauphine.fr/handle/123456789/20148
Collections
  • CEREMADE : Publications
Metadata
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Author
Mansour, Meriam
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Lépinette, Emmanuel
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Document de travail / Working paper
Item number of pages
10
Abstract (EN)
In this paper, we introduce two new concepts of conditional random set in a Banach space: The conditional interior and the conditional closure. The conditional interior is an open version of the conditional core, as recently introduced by Lépinette and Molchanov, and may be seen as a measurable version of the topological interior. The conditional closure generalizes the concept of conditional support. These concepts are useful for applications in mathematical finance and conditional optimization.

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