Continuous-Time Mean Field Games with Finite State Space and Common Noise

dc.contributor.authorBelak, Christoph
dc.contributor.authorHoffmann, Daniel
dc.contributor.authorSeifried, Frank T.
dc.date.accessioned2021-12-06T18:37:34Z
dc.date.available2021-12-06T18:37:34Z
dc.date.issued2021-02-07
dc.description.abstractWe formulate and analyze a mathematical framework for continuous-time mean field games with finitely many states and common noise, including a rigorous probabilistic construction of the state process and existence and uniqueness results for the resulting equilibrium system. The key insight is that we can circumvent the master equation and reduce the mean field equilibrium to a system of forward-backward systems of (random) ordinary differential equations by conditioning on common noise events. In the absence of common noise, our setup reduces to that of Gomes, Mohr and Souza (Appl Math Optim 68(1): 99–143, 2013) and Cecchin and Fischer (Appl Math Optim 81(2):253–300, 2020).en
dc.description.sponsorshipDFG, 264747124, GRK 2126: Algorithmic Optimization (ALOP)en
dc.description.sponsorshipTU Berlin, Open-Access-Mittel – 2021en
dc.identifier.eissn1432-0606
dc.identifier.issn0095-4616
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/13986
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-12759
dc.language.isoenen
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en
dc.subject.ddc510 Mathematikde
dc.subject.othercommon noiseen
dc.subject.otherMarkov chainsen
dc.subject.othermean field gamesen
dc.subject.otherregime shiftsen
dc.titleContinuous-Time Mean Field Games with Finite State Space and Common Noiseen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.doi10.1007/s00245-020-09743-7en
dcterms.bibliographicCitation.issue3en
dcterms.bibliographicCitation.journaltitleApplied Mathematics & Optimizationen
dcterms.bibliographicCitation.originalpublishernameSpringer Natureen
dcterms.bibliographicCitation.originalpublisherplaceNew York, NYen
dcterms.bibliographicCitation.pageend3216en
dcterms.bibliographicCitation.pagestart3173en
dcterms.bibliographicCitation.volume84en
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik::FG Finanzmathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.groupFG Finanzmathematikde
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen

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