Existence, uniqueness and comparisons for BSDEs in general spaces

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dc.contributor.authorCohen, S.
dc.contributor.authorElliott, R.
dc.date.issued2012
dc.description.abstractWe present a theory of backward stochastic differential equations in continuous time with an arbitrary filtered probability space. No assumptions are made regarding the left continuity of the filtration, of the predictable quadratic variations of martingales or of the measure integrating the driver. We present conditions for existence and uniqueness of square-integrable solutions, using Lipschitz continuity of the driver. These conditions unite the requirements for existence in continuous and discrete time and allow discrete processes to be embedded with continuous ones.We also present conditions for a comparison theorem and hence construct time consistent nonlinear expectations in these general spaces.
dc.description.statementofresponsibilitySamuel N. Cohen and Robert J. Elliott
dc.identifier.citationAnnals of Probability, 2012; 40(5):2264-2297
dc.identifier.doi10.1214/11-AOP679
dc.identifier.issn0091-1798
dc.identifier.urihttp://hdl.handle.net/2440/74759
dc.language.isoen
dc.publisherInst Mathematical Statistics
dc.relation.grantARC
dc.rights2012 © Institute of Mathematical Statistics
dc.source.urihttps://doi.org/10.1214/11-aop679
dc.subjectBSDE
dc.subjectcomparison theorem
dc.subjectgeneral filtration
dc.subjectseparable probability space
dc.subjectGrönwall inequality
dc.subjectnonlinear expectation
dc.titleExistence, uniqueness and comparisons for BSDEs in general spaces
dc.typeJournal article
pubs.publication-statusPublished

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