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hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorDumitrescu, Roxana
hal.structure.identifierLaboratoire de Probabilités et Modèles Aléatoires [LPMA]
dc.contributor.authorQuenez, Marie-Claire
hal.structure.identifierINRIA Rocquencourt
dc.contributor.authorSulem, Agnès
dc.date.accessioned2018-01-10T13:52:18Z
dc.date.available2018-01-10T13:52:18Z
dc.date.issued2016
dc.identifier.issn1083-6489
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17266
dc.language.isoenen
dc.subjectDynkin gameen
dc.subjectmixed game problemen
dc.subjectnonlinear expectationen
dc.subjectg-evaluationen
dc.subjectdoubly reflected BSDEsen
dc.subjectpartial integro-differential variational inequalitiesen
dc.subjectgame optionen
dc.subject.ddc519en
dc.titleGeneralized Dynkin games and doubly reflected BSDEs with jumpsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe introduce a game problem which can be seen as a generalization of the classical Dynkin game problem to the case of a nonlinear expectation Eg, induced by a Backward Stochastic Differential Equation (BSDE) with jumps with nonlinear driver g. Let ξ,ζ be two RCLL adapted processes with ξ≤ζ. The criterium is given by Jτ,σ=Eg0,τ∧σ(ξτ1{τ≤σ}+ζσ1{σ<τ}) where τ and σ are stopping times valued in [0,T]. Under Mokobodzki's condition, we establish the existence of a value function for this game, i.e. infσsupτJτ,σ=supτinfσJτ,σ. This value can be characterized via a doubly reflected BSDE. Using this characterization, we provide some new results on these equations, such as comparison theorems and a priori estimates. When ξ and ζ are left upper semicontinuous along stopping times, we prove the existence of a saddle point. We also study a generalized mixed game problem when the players have two actions: continuous control and stopping. We then study the generalized Dynkin game in a Markovian framework and its links with parabolic partial integro-differential variational inequalities with two obstacles.en
dc.relation.isversionofjnlnameElectronic Journal of Probability
dc.relation.isversionofjnlvol21en
dc.relation.isversionofjnlissue2016en
dc.relation.isversionofjnldate2016
dc.relation.isversionofdoi10.1214/16-EJP4568en
dc.relation.isversionofjnlpublisherElectronic Journal of Probability and Electronic Communications in Probabilityen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2018-01-10T13:49:22Z
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