Show simple item record

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorLépinette, Emmanuel*
hal.structure.identifierInstitute of Mathematical Statistics and Actuarial Science [Bern] [IMSV]
dc.contributor.authorMolchanov, Ilya*
dc.date.accessioned2020-05-06T13:22:18Z
dc.date.available2020-05-06T13:22:18Z
dc.date.issued2017
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20703
dc.language.isoenen
dc.subjectrandom set
dc.subjectselection
dc.subjectset-valued expectation
dc.subjectsublinear expectation
dc.subjectsuperlinear expectation
dc.subjectsupport function
dc.subjectessential supremum
dc.subject.ddc519en
dc.titleConditional Cores and Conditional Convex Hulls of Random Sets
dc.typeDocument de travail / Working paper
dc.description.abstractenWe define two non-linear operations with random (not necessarily closed) sets in Banach space: the conditional core and the conditional convex hull. While the first is sublinear, the second one is superlinear (in the reverse set inclusion ordering). Furthermore , we introduce the generalised conditional expectation of random closed sets and show that it is sandwiched between the conditional core and the conditional convex hull. The results rely on measurability properties of not necessarily closed random sets considered from the point of view of the families of their selections. Furthermore, we develop analytical tools suitable to handle random convex (not necessarily compact) sets in Banach spaces; these tools are based on considering support functions as functions of random arguments. The paper is motivated by applications to assessing multivariate risks in mathematical finance.
dc.publisher.cityParisen
dc.identifier.citationpages31
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris Dauphine-PSL
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01664625
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.date.updated2020-11-02T10:18:44Z
hal.author.functionaut
hal.author.functionaut


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record