Set-valued backward stochastic differential equations

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buir.contributor.authorArarat, Çağın
buir.contributor.orcidArarat, Çağın|0000-0002-6985-7665
dc.citation.epage3448en_US
dc.citation.issueNumber5
dc.citation.spage3418
dc.citation.volumeNumber33
dc.contributor.authorArarat, Çağın
dc.contributor.authorMa, J.
dc.contributor.authorWu, W.
dc.date.accessioned2024-03-13T10:59:10Z
dc.date.available2024-03-13T10:59:10Z
dc.date.issued2023-10
dc.departmentDepartment of Industrial Engineering
dc.description.abstractIn this paper, we establish an analytic framework for studying set-valued backward stochastic differential equations (set-valued BSDE), motivated largely by the current studies of dynamic set-valued risk measures for multi-asset or network-based financial models. Our framework will make use of the notion of the Hukuhara difference between sets, in order to compensate the lack of “inverse” operation of the traditional Minkowski addition, whence the vector space structure in set-valued analysis. While proving the well-posedness of a class of set-valued BSDEs, we shall also address some fundamental issues regarding generalized Aumann–Itô integrals, especially when it is connected to the martingale representation theorem. In particular, we propose some necessary extensions of the integral that can be used to represent set-valued martingales with nonsingleton initial values. This extension turns out to be essential for the study of set-valued BSDEs.
dc.description.provenanceMade available in DSpace on 2024-03-13T10:59:10Z (GMT). No. of bitstreams: 1 Set-valued_backward_stochastic_differential_equations.pdf: 428920 bytes, checksum: 75964ad4448cd8f47c78064169839c05 (MD5) Previous issue date: 2023-10en
dc.identifier.doi10.1214/22-AAP1896
dc.identifier.issn1050-5164
dc.identifier.urihttps://hdl.handle.net/11693/114676
dc.language.isoen
dc.publisherInstitute of Mathematical Statistics
dc.relation.isversionofhttps://dx.doi.org/10.1214/22-AAP1896
dc.source.titleAnnals of Applied Probability
dc.subjectConvex compact set
dc.subjectHukuhara difference
dc.subjectIntegrably bounded set-valued process Picard iteration Set-valued backward stochastic differential equation Set-valued stochastic analysis Set-valued stochastic integral
dc.subjectPicard iteration
dc.subjectSet-valued backward stochastic differential equation
dc.subjectSet-valued stochastic analysis
dc.subjectSet-valued stochastic integral
dc.titleSet-valued backward stochastic differential equations
dc.typeArticle

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