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Type: Journal article
Title: Existence, uniqueness and comparisons for BSDEs in general spaces
Author: Cohen, S.
Elliott, R.
Citation: Annals of Probability, 2012; 40(5):2264-2297
Publisher: Inst Mathematical Statistics
Issue Date: 2012
ISSN: 0091-1798
Statement of
Samuel N. Cohen and Robert J. Elliott
Abstract: We 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.
Keywords: BSDE
comparison theorem
general filtration
separable probability space
Grönwall inequality
nonlinear expectation
Rights: 2012 © Institute of Mathematical Statistics
DOI: 10.1214/11-AOP679
Grant ID: ARC
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